Your problem is the nested subroutine. It's a named subroutine, and it gets compiled once. It's not a reference to a sub, so no closure is created - and that's exactly what you want here. You're likely to find that the following works better:

sub extractlinks {
      my($url, $linktype) = @_;
 
      my @sublinks = ();
      my $callback = sub {
          my($tag, %attr) = @_;
          return if $tag ne $linktype;
          push(@sublinks, values %attr);
      }
 
      my $p = HTML::LinkExtor->new($callback); 
 
      my $res = $ua->request(HTTP::Request->new(GET => $url),
                             sub {$p->parse($_[0])});  
 
      my $base = $res->base;
      return map {$_ = url($_, $base)->abs; } @sublinks; 
}
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-- Abigail