From the docs for $/:

Remember: the value of $/ is a string, not a regex.

Your .* are regular expression syntax, but they are treated as a literal dot followed by a literal asterisk when assigned to the input record separator special variable.

If you want to avoid slurping your entire file into memory at once, you could operate on 3 lines at a time by creating a 3-line buffer:

use warnings;
use strict;

my @lines;
while (<>) {
    push @lines, $_;
    if ($. % 3 == 0) {
        # do something with @lines;
        @lines = ();
    }
}
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