Thank you all for your help!

I wanted to share the final script (at least at its current state) and get some feedback from you if at all possible. You can probably tell that I'm more used to writing Bash scripts, I'm sure I'm breaking a few Perl's style guidelines but here it goes. The goal

#!/bin/perl

use v5.36;
use strict;
use warnings;

use Getopt::Long qw/GetOptions/;

my %files_with_matches = ();

my %options = (
    'line_numbers' => 0,
    'files_with_matches' => 0,
    'print_filename' => -1,
);

sub parse_args {
    GetOptions(
       'line-numbers' => \$options{line_numbers},
       'files-with-matches' => \$options{files_with_matches},
       'print-filename!' => \$options{print_filename},
    );

    if (!@ARGV or $ARGV[0] eq "-") {
        $options{line_numbers} = 0;
        $options{files_with_matches} = 0;
        $options{print_filename} = 0;
    } else {
        my $total_files = scalar @ARGV;

        # -1 indicates this option was not modified. Fallback to
        # default values depending on how many files are provided.
        if ($options{print_filename} == -1) {
            $options{print_filename} = $total_files == 1 ? 0 : 1;
        }
    }
}

# see: https://www.rfc-editor.org/rfc/rfc3986#appendix-A

my $hexdig  = qr/[a-f0-9]/i;
my $pct_encoded = qr/%${hexdig}{2}/;
my $unreserved  = qr/[a-z0-9\-\._~]/i;
my $sub_delims  = qr/[!\$&'\(\)\*\+,;=]/;
my $pchar   = qr/(${unreserved}|${pct_encoded}|${sub_delims}|:|\@)/n;
my $dec_oct = qr((\d)|(\d\d)|(1\d\d)|(2[0-4]\d)|(25[0-5]))n;
my $ipv4    = qr(${dec_oct}\.${dec_oct}\.${dec_oct}\.${dec_oct});
my $h16     = qr(${hexdig}{1,4});
my $ls32    = qr((${h16} : ${h16}) | ${ipv4})xn;
my $ipv6    = qr(
        (                                 (${h16} :){6} ${ls32})
        | (                           ::  (${h16} :){5} ${ls32})
        | ((                ${h16})?  ::  (${h16} :){4} ${ls32})
        | (((${h16} :){0,1} ${h16})?  ::  (${h16} :){3} ${ls32})
        | (((${h16} :){0,2} ${h16})?  ::  (${h16} :){2} ${ls32})
        | (((${h16} :){0,3} ${h16})?  ::  (${h16} :){1} ${ls32})
        | (((${h16} :){0,4} ${h16})?  ::                ${ls32})
        | (((${h16} :){0,5} ${h16})?  ::                ${h16} )
        | (((${h16} :){0,6} ${h16})?  ::                       )
)xn;
my $ipvf  = qr/v${hexdig}{1,}\.(${unreserved}|${sub_delims}|:){1,}/xn;
my $ip_literal = qr{\[(${ipv6}|${ipvf})\]}n;

my $re = qr(
    \b(
        ([a-z][a-z0-9+-.]*)
        ://
        (
            (
                (${unreserved}|${pct_encoded}|${sub_delims}|:)*@
            )?
            (
                ${ip_literal}
                | ${ipv4}
                | (${unreserved}|${pct_encoded}|${sub_delims})*
            )
            (:\d+)?
        )
        (
            (\/ ( ${pchar}+(\/ ${pchar}*)*)?)
            | (\/ ${pchar}*)*
            | (${pchar}+(\/ ${pchar}*)*)
            | (${pchar}{0})
        )
        (\?(${pchar}|\/|\?)*)?
        (\#(${pchar}|\/|\?)*)?
    )\b
)xin;

sub match_url {
    my $row = shift;
    my $file = shift;
    while ($row =~ /$re/g) {
        if ($options{files_with_matches}) {
            if (! $files_with_matches{$file}) {
                $files_with_matches{$file} = 1;
                say $file;
            }
            return;
        }

        print "$file " if $options{print_filename};
        print "$. " if $options{line_numbers};
        say "$&";
    }
}

sub main {
    parse_args();

    if (!@ARGV or $ARGV[0] eq "-") {
        chomp(@ARGV = <STDIN>);
        match_url($_) for @ARGV;
        return;
    }

    # I went back to this form instead of while(<>) as I wanted to
    # provide the filename to the match_url subroutine. This was the
    # only way I knew how to do that.
    foreach (@ARGV) {
        open my $fh, '<', $_ or die("Error opening file $_ ($!)\n");
        while (my $row = <$fh>) {
            chomp $row;
            match_url($row, $_);
        }
        close($fh);
    }
}

main();
[download]

EDIT: Fixed the issue, script works now perfectly (as far as I can tell anyway :D)