You have this:

my @tokens = get_tokens $string;

my sub parse_list {
    state @tokens = @_;
    my @list;
    while (my $token = shift @tokens) {
        if ($token eq '(') {
            push @list, __SUB__->();
        } elsif ($token eq ')') {
            return \@list;
        } else {
            push @list, $token;
        }
    }
    return \@list;
}

my $list = parse_list @tokens;
[download]

Sometimes you pass tokens to it. Sometimes you don't. That's weird and confusing. Fixed:

my @tokens = get_tokens $string;

my sub parse_list {
    my @list;
    while (my $token = shift @tokens) {
        if ($token eq '(') {
            push @list, __SUB__->();
        } elsif ($token eq ')') {
            return \@list;
        } else {
            push @list, $token;
        }
    }
    return \@list;
}

my $list = parse_list;
[download]

The lack of error checking is disturbing. Fixed:

my @tokens = get_tokens $string;

my sub parse_list {
   my @list;
   while ( @tokens && $tokens[0] ne ")" ) {
      my $token = shift( @tokens );
      if ( $token eq "(" ) {
         push @list, __SUB__->();
         die( "Missing `)`" ) if !@token;
         my $token = shift( @tokens );
         die( "Missing `)`" ) if $token ne ")";
      }  else {
         push @list, $token;
      }
   }

   return \@list;
};

my $list = parse_list();
die( "Unexpected `$tokens[0]`" ) if @tokens;
[download]

Without recursion:

my @tokens = get_tokens $string;

my sub parse_list {
   my @stack;
   push @stack, [ ];
   while ( @tokens ) {
      my $token = shift( @tokens ) {
           
      if ( $token eq "(" ) {
         my $sublist = [ ];
         push @{ $stack[ -1 ] }, $sublist;
         push @stack, $sublist;
      }
      elsif ( $token eq ")" ) {
         die( "Unexpected `)` ) if @stack == 1;
         pop( @stack );
      }
      else {
         push @{ $stack[ -1 ] }, $token;
      }
   }

   die( "Missing `)` ) if @stack > 1;
   return $stack[ 0 ];
}

my $list = parse_list();
die( "Unexpected `$tokens[0]`" ) if @tokens;
[download]

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