Canonically, if you are trying to get the text output of a forked process, I understand that backlinks are needed for this. If you need an exit status, you can check it with the special $?after variable , for example:
open my $fh, '>', "output.txt" or die $!;
print {$fh} `echo "Hello!"`;
print "Return code: $?\n";
Exiting STDERR from a command in backticks will not be captured, but instead will be written directly to STDERR in the Perl program from which it called.