Untested, but I've written something similar before:

sub dev_ino_of_handle { join " ", (stat shift)[0, 1] }
sub send_maybe_both {
  my $text = shift;
  print STDOUT $text;
  print STDERR $text unless dev_ino_of_handle(\*STDOUT) eq dev_ino_of_
+handle(\*STDERR);
}
...
send_maybe_both("HEY!\n");
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