Python 3.8 (pre-release), 114 bytes

for x in[a:='for x in[a:=%r,~(i:=-1)]:##\\',~(i:=-1)]:##\
 exec(b:="x or input(a%a*i+'\\n exec(b:=%r)'%b*i);i+=1")

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Try it Try it online!online!

Try it Try it Try it online!online!online!

Tcl, 12 bytes

puts {}     

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It's just another language that also has this.

dc, 4 bytes

 []p

Similar to some other answers, since strings in dc have start ([) and end (]) delimiters (that is, " doesn't perform both duties, etc.), they're nestable without any real effort. p to print.

N=1: Try it online!

N=2: Try it nested!

N=3: Try it nesteder!

DipDup, 2 bytes

[]

It pushes the list onto the stack, and prints it without the outmost brackets.

N = 1: Try it online!

N = 2: Try it online!

N = 3: Try it online!

JavaScript, 36 32 bytes

Takes advantage of the fact that Function.prototype.toString() takes no arguments and will therefore ignore any that are passed to it.

Partly inspired by user202729's solution.

f=_=>f.toString( ).slice(14,-16)

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o.innerHTML=["<span>Five</span>",(f=_=>f.toString(f=_=>f.toString(f=_=>f.toString(f=_=>f.toString(f=_=>f.toString( ).slice(14,-16) ).slice(14,-16) ).slice(14,-16) ).slice(14,-16) ).slice(14,-16))(),"<span>Four</span>",(f=_=>f.toString(f=_=>f.toString(f=_=>f.toString(f=_=>f.toString( ).slice(14,-16) ).slice(14,-16) ).slice(14,-16) ).slice(14,-16))(),"<span>Three</span>",(f=_=>f.toString(f=_=>f.toString(f=_=>f.toString( ).slice(14,-16) ).slice(14,-16) ).slice(14,-16))(),"<span>Two</span>",(f=_=>f.toString(f=_=>f.toString( ).slice(14,-16) ).slice(14,-16))(),"<span>One</span>",(f=_=>f.toString( ).slice(14,-16))(),"<span>Thunderbirds Are Go!</span>"].join`\n`

span{font-weight:bold;font-size:16px;line-height:1.5em;text-transform:uppercase;}span:last-child{font-size:8px;}

<pre id=o></pre>

Underload, 4 bytes

N=1: Try it online.

 ()S

N=2: Try it online.

 ( ()S)S

N=3: Try it online.

 ( ( ()S)S)S

Explanation:

Self-explanatory, but I add it anyway.

• (...)S prints anything between the parenthesis to STDOUT
• The space before it is a no-op to make the byte-count even and comply to the rules of the challenge.

JavaScript (Node.js), 46 bytes

Full program. So console.log is necessary.

Use an idea from this answer to save some bytes.

l=console.log;   g=_=>{};l((''+g).slice(4,-1))

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My approach is similar to that used in Kevin Cruijssen's answer, find a nestable structure (a function in this case).

Jelly, 16 bytes

Ṿḣ-9Ḋð}“““““““““

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Doubled: Try it online!

Tripled: Try it online!

Jelly doesn't have any nestable structure, but its string literals are auto-terminated.

Ṿḣ-9Ḋ    First chain. (monadic)
Ṿ        UneṾal. (to string)
 ḣ-9     Take the ḣead, ends at the -9'th character.
    Ḋ    Ḋequeue, remove the first character.

     ð             Terminate the first chain, start a new one.
      }            Convert the last monadic chain to a dyadic one.
       “““““““““   String literal.
                   This matches the pattern <dyad> <nilad>, so applies
                   the the corresponding rules. This way a link can take data
                   to the right of it.

Will try different approaches to see if they can be shorter.