Your requirements are not crystal clear to me. I see that your original program (turned into a Short, Self-Contained, Correct Example):

use strict;
use warnings;
use Data::Dumper;

my $path = '/.snapshots123/yabsm/root/hourly/day=2021_03_04,time=21:20
+';

my $end_of_path;
$end_of_path = $1 if $path =~ m/([^\/]+$)/;

my @nums = $end_of_path =~ m/([0-9]{2,4})/g;
print Dumper( \@nums );
[download]

prints:

$VAR1 = [
          '2021',
          '03',
          '04',
          '21',
          '20'
        ];
[download]

... as does my simpler version:

use strict;
use warnings;
use Data::Dumper;

my $path = '/.snapshots123/yabsm/root/hourly/day=2021_03_04,time=21:20
+';

my @nums = $path =~ m{/day=(\d\d\d\d)_(\d\d)_(\d\d),time=(\d\d):(\d\d)
+$};
print Dumper( \@nums );
[download]

Does my version satisfy your requirements?