Looping over elements in an array and then changing the number of elements in that array can have unexpected results. Here's a quick fix:

while (@files) {
    my @bb;
    for (1 .. $num_cols) {
        my $file = shift @files || last;
        push @bb, $file;
    }
    push @data, \@bb;
}
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I chose while for this so that the loop will only continue while there are still elements in @files. I use the shift-or construct just in case the number of elements in @files is not a multiple of $num_cols. I push a reference onto @data because it's conceptually clearer to me (and it doesn't expand @bb into a list and then make that into an anonymous list).

splice is your best solution, though.