use v5.12;
use warnings;

my $h = {
    'connection-id0' => {
        username1 => ['value 1', 'value 2'],
        username2 => [ 'value5' ],
    },
    'connection-id1' => {
        username1 => ['value 2', 'value 3'],
    },
    'connection-id2' => {
        username1 => ['value 3', 'value 4'],
    }
};

while ( my ( $con, $h_users) = each %$h ){
    while ( my ($user, $a_vals) = each %$h_users ) {
        my $val = $a_vals->[1] // "";
        say "Found $con -> $user -> $val"
          if $val =~ /value/;
    }
}
[download]

Found connection-id2 -> username1 -> value 4
Found connection-id1 -> username1 -> value 3
Found connection-id0 -> username1 -> value 2
[download]