I updated the code somewhat to allow it to run on my slightly older (5.34) Perl.
I also added an additional method (kco3) as my preferred way to write your version of the code.

#!/usr/bin/env perl

#use v5.38;
use feature qw|say|;
use autodie;
use constant {
    SEP1 => "\n" . '=' x 40,
    SEP2 => '-' x 40,
};

use Benchmark 'cmpthese';
use File::Spec ();

my ($null_fh, $base_str);
BEGIN {
    open $null_fh, '>', File::Spec::->devnull();
    $base_str = <<~'EOT';
        AdataA
        BdataB
        CdataC
        EOT
}

my @bench_names = qw{net1 net2 hau1 ner1 ner2 kco1 kco2 kco3};
my (%bench_for, %benches_to_cmp, $mult_str);
say 'Test', SEP1;

for my $bench (@bench_names) {
    no strict 'refs';
    ($bench_for{$bench} = \&{$bench})->(\$base_str);
    use strict 'refs';
    say SEP2;

    $benches_to_cmp{$bench} = sub {
        $bench_for{$bench}->(\$mult_str, $null_fh);
    };
}

for my $mult (1, 10, 100, 1_000, 10_000) {
    $mult_str = $base_str x $mult;
    say 'Bench (Length: ', length($mult_str), ')', SEP1;
    cmpthese 0 => \%benches_to_cmp;
    say SEP2;
}

sub net1 ($rstr, $out_fh = *STDOUT) {
    my $str = $$rstr;

    while ($str =~ /(^A|^B)(.+)$/mg){
        $out_fh->say("$1 net1 $2");
    }

    return;
}

sub net2 ($rstr, $out_fh = *STDOUT) {
    my $str = $$rstr;

    open my $fh, '<', \$str;

    while (<$fh>) {
        my ($name, $data) = m/(^A|^B)(.+)$/ or next;
        $out_fh->say("$name net2 $data");
    }

    return;
}

sub hau1 ($rstr, $out_fh = *STDOUT) {
    my $str = $$rstr;

    while ($str =~ m{^ (?<name>A|B) (?<data>.+) $}xmg) {
        $out_fh->say("$+{name} hau1 $+{data}");
    }

    return;
}

sub ner1 ($rstr, $out_fh = *STDOUT) {
    my $str = $$rstr;

    $out_fh->say("$1 ner1 $2") while $str =~ /^([AB])(.+)$/mg;

    return;
}

sub ner2 ($rstr, $out_fh = *STDOUT) {
    my $str = $$rstr;

    $str =~ /^([AB])(.++)$(?{ $out_fh->say("$1 ner2 $2") })./m;

    return;
}

sub kco1 ($rstr, $out_fh = *STDOUT) {
    my $str = $$rstr;
    my $re = qr{(?m:^([AB])(.+)$)};

    $out_fh->say("$1 kco1 $2") while $str =~ /$re/g;

    return;
}

sub kco3 ($rstr, $out_fh = *STDOUT) {
    my $str = $$rstr;
    my $re = qr{(?m:^(A|B)(.+)$)};

     while ($str =~ /$re/go){
        $out_fh->say("$1 kco2 $2") ;
     }

    return;
}


sub kco2 ($rstr, $out_fh = *STDOUT) {
    my $str = $$rstr;
    my $re = qr{(?m:^([AB])(.+)$)};

    $out_fh->say("$1 kco2 $2") while $str =~ /$re/go;
[download]

$ perl pm-11154897.pl
Test
========================================
----------------------------------------
----------------------------------------
----------------------------------------
----------------------------------------
----------------------------------------
----------------------------------------
----------------------------------------
----------------------------------------
Bench (Length: 21)
========================================
          Rate  net2  kco1  kco2  kco3  net1  ner1  hau1  ner2
net2  260654/s    --  -90%  -92%  -92%  -97%  -97%  -97%  -97%
kco1 2536874/s  873%    --  -20%  -21%  -68%  -69%  -70%  -71%
kco2 3178301/s 1119%   25%    --   -1%  -60%  -61%  -62%  -64%
kco3 3207697/s 1131%   26%    1%    --  -59%  -61%  -62%  -63%
net1 7889843/s 2927%  211%  148%  146%    --   -4%   -5%  -10%
ner1 8226198/s 3056%  224%  159%  156%    4%    --   -1%   -6%
hau1 8333730/s 3097%  229%  162%  160%    6%    1%    --   -5%
ner2 8767731/s 3264%  246%  176%  173%   11%    7%    5%    --
----------------------------------------
Bench (Length: 210)
========================================
          Rate  net2  kco1  kco3  kco2  net1  hau1  ner1  ner2
net2  260526/s    --  -90%  -92%  -92%  -97%  -97%  -97%  -97%
kco1 2492787/s  857%    --  -20%  -20%  -68%  -69%  -69%  -71%
kco3 3114015/s 1095%   25%    --   -0%  -60%  -61%  -61%  -64%
kco2 3123870/s 1099%   25%    0%    --  -60%  -61%  -61%  -64%
net1 7758408/s 2878%  211%  149%  148%    --   -3%   -3%  -10%
hau1 7965224/s 2957%  220%  156%  155%    3%    --   -0%   -7%
ner1 7965224/s 2957%  220%  156%  155%    3%    0%    --   -7%
ner2 8601600/s 3202%  245%  176%  175%   11%    8%    8%    --
----------------------------------------
Bench (Length: 2100)
========================================
          Rate  net2  kco1  kco2  kco3  hau1  net1  ner1  ner2
net2  257948/s    --  -90%  -92%  -92%  -97%  -97%  -97%  -97%
kco1 2501079/s  870%    --  -19%  -20%  -67%  -68%  -68%  -71%
kco2 3097753/s 1101%   24%    --   -1%  -59%  -60%  -60%  -64%
kco3 3133787/s 1115%   25%    1%    --  -58%  -60%  -60%  -64%
hau1 7510752/s 2812%  200%  142%  140%    --   -3%   -4%  -13%
net1 7771227/s 2913%  211%  151%  148%    3%    --   -0%  -10%
ner1 7794563/s 2922%  212%  152%  149%    4%    0%    --  -10%
ner2 8628990/s 3245%  245%  179%  175%   15%   11%   11%    --
----------------------------------------
Bench (Length: 21000)
========================================
          Rate  net2  kco1  kco2  kco3  net1  ner1  hau1  ner2
net2  231838/s    --  -91%  -93%  -93%  -97%  -97%  -97%  -97%
kco1 2478677/s  969%    --  -20%  -22%  -67%  -68%  -69%  -70%
kco2 3094492/s 1235%   25%    --   -3%  -59%  -61%  -62%  -63%
kco3 3178304/s 1271%   28%    3%    --  -58%  -59%  -61%  -62%
net1 7593413/s 3175%  206%  145%  139%    --   -3%   -6%   -9%
ner1 7840377/s 3282%  216%  153%  147%    3%    --   -3%   -6%
hau1 8068001/s 3380%  225%  161%  154%    6%    3%    --   -4%
ner2 8382339/s 3516%  238%  171%  164%   10%    7%    4%    --
----------------------------------------
Bench (Length: 210000)
========================================
          Rate  net2  kco1  kco2  kco3  hau1  ner1  net1  ner2
net2  250558/s    --  -85%  -89%  -92%  -96%  -97%  -97%  -97%
kco1 1640135/s  555%    --  -28%  -46%  -75%  -78%  -78%  -81%
kco2 2269326/s  806%   38%    --  -25%  -66%  -70%  -70%  -73%
kco3 3032215/s 1110%   85%   34%    --  -54%  -59%  -60%  -65%
hau1 6657718/s 2557%  306%  193%  120%    --  -11%  -13%  -22%
ner1 7484171/s 2887%  356%  230%  147%   12%    --   -2%  -13%
net1 7612303/s 2938%  364%  235%  151%   14%    2%    --  -11%
ner2 8558296/s 3316%  422%  277%  182%   29%   14%   12%    --
----------------------------------------
[download]