So here's what I think you could best do:

Read both files line by line, and for each line:

1. split into date+timestamp on one hand, and data on the other:

   my($datetime, $data) = /^(\w+-\d+,[\d:.]+),(.*)/;
   [download]

2. push the $data onto an arrayref that's the value in global hash for that $datetime:

   push @{ $data{$datetime} }, $data;
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   Note that autovivification makes it unnecessary to create the arrayref before you do this.

OK, so you now have the data in the hash in a form directly usable for your output. One major problem is that hash keys are unordered, so you'll have to sort them. If all dates are the same, a simple alphanumerical sort will sort them by timestamp:

foreach my $key (sort keys %data) { ...
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You can simply join the values in the anonymous array, with a comma:

    print $key, ',', join(',', @{ $data{$key} }), "\n";
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And that should be close!

The whole program:

#! perl -w

@ARGV = ('file1.txt', 'file2.txt');
my %data; 
while(<>) {
    my($datetime, $data) = /^(\w+-\d+,[\d:.]+),(.*)/;
    push @{ $data{$datetime} }, $data;
}
foreach my $key (sort keys %data) {
    print $key, ',', join(',', @{ $data{$key} }), "\n";
}
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Feb-21,19:08:05.2,$GP,48.96,90.92,45.69,$BM,3.89
Feb-21,19:08:06.4,$GP,48.92,90.92,45.70
Feb-21,19:08:07.6,$GP,48.93,90.99,45.66,$BM,6.20
Feb-21,19:08:08.1,$GP,48.92,90.95,45.66
Feb-21,19:08:09.0,$GP,48.85,90.92,45.62,$BM,8.52
Feb-21,19:08:10.8,$GP,48.92,90.94,45.63,$BM,9.68
Feb-21,19:21:20.5,$BM,5.05
Feb-21,19:21:20.8,$BM,7.36
[download]

Thank you very much for your time. It helps me a lot.