I am getting the original sorting of the list.

Because your sub doesn't return the transformed string; it returns the result of the the last transform. Change that to:

sub transform{
    my $string = shift;
    $string =~ tr/A-Z/a-z/;#kleinschreibung
    $string =~ tr/a-z//cd;
    $string; 
}
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(As an aside; are you aware that for my $word (@output){say $word;} is more easily written as say for @output?)