use feature 'current_sub';

... as directed in the documentation.

Or use v5.16;.

perl did not mention it's a feature, when using refaliasing without declare it got smarter. Now it's all good.

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]

add some check is good, and need to point at wrong line.

package MyPairList;
use strict;
use warnings;
use feature 'state';
use Data::Dumper;
use List::Util qw(all none);
use Exporter 'import';
use feature 'current_sub';
our @EXPORT = qw(pair_list_parse);

sub pair_list_parse {
my $string = shift;
my sub get_tokens {
    my $string = shift;
    my @tokens = $string =~ /([()\n]|[^()\s]+)/g;
}
my @tokens = get_tokens $string;

my sub check_tokens {
   my $line;
   my @line;
   for my $token (@tokens) {
       if ($token eq "\n") {
           $line++;
           my $left = scalar grep {$_ eq '('} @line;
           my $right = scalar grep {$_ eq ')'} @line;
           my $is_open = $line[-1] eq '(';
           my $is_all_right = $right && not $left;
           my $is_closed = $right == $left;
           die "config line $line wrong" unless ( $is_open or $is_all_
+right or $is_closed);
           @line = ();
       } else {
           push @line, $token
       }
   }
}
check_tokens;

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

my $list = parse_list;

my sub parse_nested_list {
    my ($list) = @_;
    my %hash;
    if (none {ref $_} @$list) {
      if (@$list == 1) {
        return $list->[0];
      } elsif (@$list == 2) {
        return { $list->[0] => $list->[1] };
      } else {
        return $list
      }
    } elsif (all {ref $_} @$list) {
        return [ map { __SUB__->($_) } @$list ];
    } else {
        my ($key, $ref, @remain) = @$list;
        die 'wrong key ', Dumper $key if ref $key;
        die 'wrong value ', Dumper $ref unless ref $ref;
        die 'redundant value', Dumper \@remain if @remain;
        $hash{$key} = __SUB__->($ref);
    }
    return \%hash;
}
return parse_nested_list($list)
}
1;
[download]

Every line can only brankets closed if not open or pure ')'