Japt, 40 39 38 37 bytes

This version has a very high probability of having all 4 layers, using a similar approach as Level's Ruby solution of generating all 4 layers, removing the ones consisting entirely of empty quadrants and making a recursive call if there are none left.

ªß4Æ"RWCS"ï`Õ½wbgp` p-² ö4 qÃfÈr-Ãq':

Test it

Wolfram Language (Mathematica), 155 bytes

r=RandomInteger
c=RandomChoice
t=Table
StringRiffle[StringJoin/@(Nest[#/.c@#->"--"&,#,r@2]&/@t[t[#<>#2&@@c@*Characters/@{"RWSC","urgbypcw"},4],r@3+1]),":"]

The distribution of the non-empty quadrants is uniform, but the distribution of shapes is not, as empty quadrants are generated after the fact.

TIO requires two extra bytes for symbol assignment so that the output can be printed.

Try it online!

FMSLogo, 106 bytes

show bl map[word pick bf invoke[(crossmap "word ? ? ? ?)]se[--]crossmap "word[RWCS urgbycpw]":]random 1500

Don't try it online. The calormen.com logo interpreter does not support "templates" (which is what logo calls anonymous functions) on map, only procedure names; it's error messages also leave something to be desired. The program works in FMSLogo 8.3.2 and propably MSWLogo and UCBLogo as well, as FMSLogo is based on them.

Explaination:

• Logo is based on lisp but allows omitting parentheses around procedures that use their default arity.
• crossmap generates all possible combinations of the members of its inputs, which can be given in a list. The first input is a function, or "template", which is passed each combination to combine them.
• I don't know a better way to remove the empty layer yet, so the first crossmap generates a 1185921 element list of every possible layer and then bf removes the first one. That's why this program takes approximately 27 seconds to run on my laptop.
• Numbers can be coerced to strings in logo, so map maps the big instruction list in the middle over the characters of a random number, which has some length between one and four. repeat 1+random 4[...] would not output the concatenation of the results, and using map[...]iseq random 4 4 is 4 characters longer.
• I would not be able to tell, of course, but maybe some correlation in the random number generator makes some shapes actually impossible. I am not going to investigate.

Anonymous functions can not be called the normal way, unlike in javascript for example. They must be called by apply, map, or similar, which is why I consider

[bl map[word pick bf invoke[(crossmap "word ? ? ? ?)]se[--]crossmap "word[RWCS urgbycpw]":]random 1500]

to be an invalid submission.

Alternative much faster 5 characters longer solution, which, unlike the submission, can propably produce empty output:

FMSLogo, 111 bytes

show bl map[invoke[if ?="--------: ["][?]]word map[pick se[--]crossmap "word[RWCS urgbcypw]]1234 ":]random 1500

Sample shape: CpCuRpSc:SwSuCcWr:Sb--RwSb (everyone seems to do this)

Bash, 158 bytes

p='eval printf %s, '
s=$($p {S,W,C,R}{u,g,b,r,y,c,p,w})--
l=`$p{$s}{$s}{$s}{$s}`
$p{$l}:{$l}:{$l}:{$l}|tr , \\n|sed -E "s/-{4}(:|$)//g;/(^|:)(:|$)/d"|shuf -n1

Attempt This Online!

JavaScript (ES6), 117 bytes

-2 thanks to @l4m2

Although this is not required, this solution has a uniform distribution.

f=(k=(R=Math.random)()*4|0,q=R(n=4)*1185920)=>n--?f(k,q/33)+'SWCR-'[((q%=33)&35)%7]+'ugbrycpw-'[q>>2]:k?f(k-1)+':':''

Try it online!

JavaScript (V8), 117 116 114 bytes

f=(k=n=5*~R(4))=>++n?n%5?R(~k%5)?'--'+f(k+1):'SWCR'[R(4)]+'ugbrycpw'[R(8)]+f(k):':'+f(n):''
R=n=>Math.random()*n|0

Try it online!

If already \$k\$ empty in this layer, then there's \$\frac 1{4-k}\$ probably be not empty, aka 1 when already 3 empty

MathGolf, 49 bytes

{╘4{4{"CRSW"w"bcgpruwy"w+v¶╛æ;û--}Γy}Γ'-8*a-}↔':u

Try it online.

The first output was: CwRuRrRw:RpSwSbRp:RcWpRpCu:CpWwWgWc:

Explanation:

{ ... }↔          # Do while false without popping:
 ╘                #  Empty the stack (in case we've encountered a fully empty result)
  4{              #  Loop 4 times:
    4{            #   Inner loop 4 times:
      "CRSW"w     #    Push a random character from "CRSW"
      "bcgpruwy"w #    Push a random character from "bcgpruwy"
       +          #    Concat these two characters together
        v         #    Push a random integer in the range [-2147483648,2147483647]
         ¶╛       #    If this integer is a prime number,
           æ      #    use the following four character as inner code-block:
            ;     #     Discard the earlier character pair
             û--  #     Push "--"
     }            #   After the inner loop:
      Γ           #   Wrap the top four items into a list
       y          #   And join this list together to a single string
   }              #  After the outer loop:
    Γ             #  Wrap the top (up to) four items into a list
     '-8*a-      '#  Remove any strings consisting of 8 "-"
}↔                # After the do-while false:
  ':u            '# Join the list with ":" delimiter
                  # (after which the entire stack is output implicitly as result)

Compressed strings are pretty mediocre in MathGolf, so unfortunately it won't save any bytes here. "CRSW"w can be ╖╖`'w+wδ which is 1 byte longer, and "bcgpruwy" can be ╕█≈║☺ 'ußy which is the same byte-count.

05AB1E, 35 40 38 36 bytes

+5 to prevent empty output which would've occured with probability \$33^{-16}\$
-2 bytes thanks to Kevin Cruijssen!

Quite slow, generates \$33^4\$ possible layers 4 times and chooses a random one each time. Layers of all - are removed.

[₄ε‘¥„W‘’»Õpcw’â„--ª4ãΩJ}'-8×K':ýDĀ#

Try it online!

At the cost of two bytes this can actually run fast: Try it online!

Because every quadrant in each layer has a \$1\$ in \$33\$ chance of being empty the resulting shapes are quite noisy:

[    ...    Dg#              # until the the output is not empty, do the following:

₄                            # push constant 1000
  ε                     }    # for each digit in this number:
   ‘¥„W‘                     #   dictionary compressed string "SRCW"
        ’»Õpcw’              #   dictionary compressed string "rugbypcw"
               â             #   cartesian product of the two strings
                „--ª         #   append "--" to this list
                    4ã       #   4th cartesian power, all 4-element combinations from the length-2 strings
                      Ω      #   choose a random one
                       J     #   join into a single string

'-8×                         # string of 8 -'s
    K                        # remove all occurences from the list
     ':ý                     # join the list by ":"

Java (JDK), ²⁶³ 253 bytes

-10 thanks to ceilingcat! Forgot that | exists and that ternary ifs can be written without parentheses. D'oh!

String f(int i){var r=new Random();var q=""+"SWCR-".charAt(r.nextInt(5));q+=q.equals("-")?'-':"ugbrycpw".charAt(r.nextInt(8));return i<1?(f(2)+f(2)+f(2)+f(3)).substring(1):i<9?i>2|r.nextInt(2)<1?(":"+f(9)+f(9)+f(9)+f(9)).replace(":--------",f(1)):"":q;}

Try it online!

Took forever to find something promising, ow my head... This won't win any prices, but I liked the approach so here it is anyways. It uses the same function recursively with a different parameter to build different parts of the string.
I hope I find the template for Java lambdas again, I keep forgetting how the boilerplate needs to look for them to work :(

EDIT:

Function lamdas aren't shorter in this case, since you don't call but apply() them, which is WAY longer. Still, thanks for the template Johan du Troit!

Explained:

// function is called with 0 to start
String f(int i) {
    // use var because it's shorter
    var r=new Random();

    // build a quadrant
    // decide on a type...
    var q=""+"SWCR-".charAt(r.nextInt(5));
    // ...and append the color. If the type is "-" then append a "-" instead
    q+=q.equals("-")?'-':"ugbrycpw".charAt(r.nextInt(8));
    
    // decide what to return
    return 
    // shape case: build full shape
    i<1?
      // a shape consists of four layers
      // each layer starts with a :, cut the first one off
      (f(2)+f(2)+f(2)+f(3)).substring(1)

    // not the starting case, check for layer case
    :i<9?
      // build one layer. It either doesn't exist or contains four shapes
      // note: 3 overrides the random decision and always returns a layer
      i>2|r.nextInt(2)<1?
        // replace an empty layer with a newly generated one...
        (":"+f(9)+f(9)+f(9)+f(9)).replace(":--------",f(1)) 
        // ...or return a nonexistant layer
        :""
    // not the shape case nor the layer case, return the quadrant calculated above
    :q;
}

CSASM v2.5.1, 514 bytes

func a:
lda 0
sta $1
lda ""
sta $2
push 1
push 5
extern Random.Next(i32,i32)
pop $a
.lbl a
push $a
brfalse b
dec $a
push 0
pop $1
push ""
pop $3
.lbl c
push $1
push 4
sub
brfalse d
inc $1
push "RWSC-"
push 5
extern Random.Next(i32)
dup
push 1
add
substr
dup
push "-"
sub
len
brtrue f
dup
add
br e
.lbl f
push "urgbypcw"
push 8
extern Random.Next(i32)
dup
push 1
add
substr
add
.lbl e
push $3
swap
add
dup
pop $3
push "--------"
sub
len
brtrue c
push 0
pop $1
push ""
pop $3
br c
.lbl d
push $2
push $3
add
pop $2
push $a
brfalse a
push $2
push ":"
add
pop $2
br a
.lbl b
push $2
print
ret
end

Whew, this was one mammoth of a program to write.

This submission defines a function a which generates then prints the random shape string as is specified by the challenge.

Explained:

func a:
    ; $a = random value in [1, 4]
    ; $1 = loop counter for quadrants
    ; $2 = final string
    ; $3 = build string
    lda 0
    sta $1

    ; Initialize $2 to an empty string
    lda ""
    sta $2
    
    ; Initialize $a to the random value specified above
    push 1
    push 5
    extern Random.Next(i32,i32)
    pop $a

    .lbl a
        ; Stop looping if $a == 0
        push $a
        brfalse b
        dec $a

        ; Reset $1 and $3
        push 0
        pop $1
        push ""
        pop $3

        .lbl c
            ; Stop looping if $1 == 4
            push $1
            push 4
            sub
            brfalse d
            inc $1
            
            ; Get a random letter in "RWSC-"
            push "RWSC-"
            push 5
            extern Random.Next(i32)
            dup
            push 1
            add
            substr

            ; Check if the letter was "-"
            dup
            push "-"
            sub
            len
            brtrue f
            ; Letter was "-"; just add the other one
            dup
            add
            br e
        .lbl f
            ; Letter was not "-"; Get the color
            push "urgbypcw"
            push 8
            extern Random.Next(i32)
            dup
            push 1
            add
            substr

            ; Add the two parts together
            add
        .lbl e
            ; Add the new piece to $3
            push $3
            swap
            add
            dup
            pop $3

            ; Check $3.  If it's "--------", generate another layer
            push "--------"
            sub
            len
            brtrue c
            
            ; Reset the quadrants counter and build string
            push 0
            pop $1
            push ""
            pop $3

            br c
        .lbl d
            ; Append the layer to the result
            push $2
            push $3
            add
            pop $2
            
            ; If $a == 0, don't add the ":"
            push $a
            brfalse a
            push $2
            push ":"
            add
            pop $2
            br a
.lbl b
    ; Print the result
    push $2
    print
    ret
end

The first run of this code produce the following shape:
--Cp----:--RgSg--:CgRwWbRr:WyWpWwWw

More examples of shapes generated by the code:

--ScWyRp
WuWuCbRg:--RbSwRc:CwRuWrCb
CgSgRpCb:Cu--SrRb
Wc--CcCg:----CrRu
SyCbWc--
SrCbSc--:----WrWb
Ry--CgSr:--Cp--Sw
--CwWpCc:CbCpRcSy:CpWw--Cy:--Ru----

Python 3, 129 bytes

from random import*
print(':'.join(''.join(sample(q,4))for q in[[i+j for i in'RWSC'for j in'urgbypcw']*4+['--']*3]*randint(1,4)))

Try it online!

For each layer, 4 items are picked from a distribution containing 3 empty quadrants and the other shape-colour combinations 4 times.

Perl 5, 95 138 bytes

{@q=(qw(: --),map{$s=$_;map$s.$_,ugbrycpw=~/./g}C,R,W,S);@i=map$_%5?$==1+rand
33:0,1..rand 19;@i%5==4&&" @i "!~/ (1 ){4}/||redo;say@q[@i]}

Try it online!

C#_[9.0] - 191, 235, 228, 204, 203 Bytes (Condensed)

static Random r=new();static string g(){var z="";for(int j,i,l=r.Next(1,4);l-->0;z+=":")for(i=j=0;i++<4;)z+=r.Next()%8<1&&j++<3?"--":$"{"CRWS"[r.Next(0,3)]}{"rgbypcuw"[r.Next(0,7)]}";return z.Trim(':');}

• +44 bytes due to a missed requirement.
• -5 bytes by reducing GetShape to g per @emanresu A's recommendation.
• -24 bytes by using var, consolidating declarations and using constant strings per @Johan du Toit.
• -1 byte by swapping ==0 for <1 per @ceilingcat.

How it Works

// Create a new random number generator using C# 9.0's `new` invocation.
static Random r = new();
static string g() {

    // Create a variable to store the possible shapes.
    string s = "CRWS",

            // Create a variable to store the possible colors.
            c = "rgbypcuw",

            // Create a variable to store the result.
            z = "";

    // Create an iteration variable to iteratively create between 1 and 4 layers randomly.
    // Evaluate for stop then decrement.
    // Append `:` to the result.
    for (int l = r.Next(1, 4); l-- > 0; z+=":")

        // Create an iteration variable to iteratively create the four quadrants.
        // Create a variable for tracking the number of empty quadrants.
        for (int i = 0, j = 0; i++ < 4;)

            // If we haven't reached the maximum number of allowed empty quadrants, a new one can still be added.
            // Use a random number to determine if we should create an empty quadrant.
            // Since && short circuits, the increment of J doesn't occur unless we're adding an empty quadrant.
            if (r.Next() % 8 == 0 && j++ < 3)

                // Add an empty quadrant.
                z += "--";

            // Otherwise, add a shape and color from the variables above,
            //      using a random index within the bounds of the variables lengths.
            else
                z += $"{s[r.Next(0, 3)]}{c[r.Next(0, 7)]}";

    // Return the result and remove any trailing `:`.
    return z.Trim(':');
}

Sample Output

I called the method in a for loop over 10 iterations to sample the output for this post:

--CyCpCb:RpCu--Rc
RpCyWbWc:RcWuWyWc
CyWy--Cr:RrWpWuWg
Wp--WuRc
RpCcCgWp
CbWuWgCu:--RcRbWg:CcCuCpCc
RgRpCyCu:CbWyWuCu
CgCuRpCu
CyRc--Ru:WuRuRbRu:--CgRbWr
WpCgCpRu

Resulting Image Sample

I ran the shape code CbWuWgCu:--RcRbWg:CcCuCpCc through and got this result:

C (gcc), 137 bytes

#define r rand()
m;b;q(){m=r;m&30||q();}f(){for(q(b=5+r%4*5);--b;)printf(b%5?m&1<<b%5?"%c%c":"--":":"+!q(),"WRSC"[r%4],"rugbywcp"[r%8]);}

Try it online!

-5 bytes thanks ceilingcat!

JavaScript, 125 120 119 115 112 118 bytes

To avoid the possibility of an empty layer, we force the 4th quadrant to be non-empty if all previous quadrants are already empty (+6 bytes 'cause I realised I'd screwed that up).

Need to figure out a way to shorten the selection of the characters.

(r=x=>Math.random(g=s=>s[7]?l--?s+`:`+g``:s:g(s+`RWSC-`[c=r(5^s==`------`)]+`urgbypcw-`[c-4?r(8):8]))*x|0,l=r(4))=>g``

Try it online!

Jelly, 38 35 34 bytes

“SWCR”p“¬,ĖṆḷ⁸»Żṗ4XʋⱮ4ẸƇƊṆ¿o⁾--j”:

Try it online!

This just about finishes on TIO most of the time (it has a \$1\$ in \$33^{16}\$ chance of taking longer), taking around 55 seconds. Full program, as we require Jelly's smash-printing to get the correct output

-4 bytes thanks to Jonathan Allan!

The first sample output I got was:

External link

How it works

“SWCR”p“¬,ĖṆḷ⁸»Żṗ4XʋⱮ4ẸƇƊṆ¿o⁾--j”: - Main link. No arguments. Left argument = 0
                        Ɗ          - Group the previous 3 links into a monad f(_): (ignores the argument)
“SWCR”                             -   Set the return value to “SWCR”
                   ʋ               -   Group the previous 4 links into a dyad g(“SWCR”, i): (ignores i)
       “¬,ĖṆḷ⁸»                    -     Compressed string: “rugbypcw”
      p                            -     Cartesian product with “SWCR”
               Ż                   -     Prepend a zero (represents “--”)
                ṗ4                 -     4th Cartesian power
                  X                -     Choose a random list
                    Ɱ4             -   Yield [g(“SWCR”,1), g(“SWCR”,2), g(“SWCR”,3), g(“SWCR”,4)]
                      ẸƇ           -   Remove any that are just zeros
                          ¿        - While:
                         Ṇ         -   The left argument is falsey ([] or 0)
                        Ɗ          -   Set the left argument to f(_)
                           o⁾--    - Replace all zeros with “--”
                               j”: - Join by ”: and smash-print

Ruby, 117 114 bytes

->{s=((0..19).map{|i|i%5<1??::"-SWCR"[(r=rand 40)/8]+"rgbpucyw-"[r<8?8:r%8]}*'').gsub ?:+?-*8,''
s>''?s[1,99]:f[]}

Try it online!

A function returning a string.

Commented code (original version)

->{s=
 ((0..19).map{|i|i%5<1?     #Iterate 20 times to make an array. if i%5==0  
 ?::                        #put a colon, else...
  "-SWCR"[(r=rand 40)/8]+   #Select a shape
  (r<8??-:"rgbpucyw"[r%8])  #If selected shape is - then put another -, else put a colour
  }*'').                    #Convert the 20-element array into a string
  gsub(?:+?-*8,'')          #Delete all instances of :--------
  s<?!?f[]:s[1,99]}         #If s is empty, recursively call f[] to try again. Else output s (minus the initial colon) 

Vyxal rR, 37 bytes

\:4℅ƛ«3⟩∑ḣ`«`SWRC`Ẋ‛--J33²²‹℅τ∑₅8ε-;j

Try it Online!

This uses a quite neat custom-base-decompression-based approach to ensure there'll never be an empty layer. It basically generates a random number between 1 and \$33^4 - 1\$, decompresses it with the key as all possible quadrants (with -- first, so 0 can never occur, so empty layers won't either).

  4℅ƛ                              ;  # array of length (random 1-4) filled with...
                       33²²‹℅         # Random integer between 1 and 33^4-1 inclusive 
                             τ        # Decompressed by...
                  Ẋ                   # Cartesian product of...
     «3⟩∑ḣ`«                          # Compressed string `bcgpruwy`
            `SWRC`                    # String literal `SWRC`
                   ‛--J               # Prepend a `--`
                              ∑       # Concatenate all this
                               ₅8ε-   # Pad with `-` from the start
                                    j # Join the whole thing by...
\:                                    # Semicolons.

APL(Dyalog Unicode), 64 bytes ^SBCS

A full program that prints the shape.

⊃{∊⍺':'⍵}/{∊((⊂'--'),,'RWCS'∘.,'urgbypcw')[?4⍴33]}⍣{∨/'-'≠⍺}¨⍳?4

Try it on APLgolf!

?4 random integer between 1 and 4
... ¨⍳ call the function on the left this many times and collect the results in a list:

{ ... }⍣{∨/'-'≠⍺} until any char in the result is not -:
'RWCS'∘.,'urgbypcw' Cartesian product of the two strings
, flatten into a list of 2-char strings
(⊂'--'), prepend the empty quadrant
( ... )[?4⍴33] get elements at 4 random indices between 1 and 33.
∊ flatten into a string

{∊⍺':'⍵}/ join with :
⊃ get the first element from the nested output

Charcoal, 51 bytes

⪫ＥＥ⊕‽⁴⊕‽⊖Ｘ³³¦⁴⭆Ｅ⁴÷ιＸ³³λ⎇﹪λ³³⁺§RWSCλ§urgbypcw÷λ⁴--¦:

Try it online! Link is to verbose version of code. Explanation:

    ‽⁴                                              Random integer 0-3
   ⊕                                                Incremented
  Ｅ                                                 Map over implicit range
         Ｘ³³¦⁴                                      33⁴
        ⊖                                           Decremented
       ‽                                            Random integer
      ⊕                                             Incremented
 Ｅ                                                  Map over random integers
               Ｅ⁴                                   Map over quadrants
                 ÷ι                                 Current random integer
                 ÷                                  Integer divide by
                    ³³                              Literal integer `33`
                   Ｘ                                Raised to power
                      λ                             Current quadrant
              ⭆                                     Map over values and join
                         λ                          Current value
                        ﹪ ³³                        Modulo literal `33`
                       ⎇                            If nonzero then
                             §RWSCλ                 Cyclically indexed colour
                            ⁺                       Concatenated with
                                   §urgbypcw        Shape cyclically indexed by
                                             λ      Current value
                                            ÷       Integer divide by
                                              ⁴     Literal integer `4`
                                               --   Else literal string `--`
⪫                                                 : Join with literal `:`
                                                    Implicitly print