This small modification makes your code work:

foreach my $line (split /^/, $text) {
    print $line;
    my $separator_printed = 0;
    foreach ($line =~ m/\[.*?\]\[(.*?)\]/g) {
        my $link_number = $_;
         $separator_printed++ or print "\n";
        print grep(/(\[$link_number\]\:.*)/, @url_list);
        print "\n";
    }
}
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