Since the pass phrase is used to protect the identity file, you could avoid the need for it by setting up the identity file to not require a pass phrase. (This will not affect the server because the server never "sees" the pass phrase.)

If that is not acceptable, then if your objective to avoid having to type in the pass phrase each time you run your Perl program, then you could use ssh-agent so you would only need to type in your phrase phase once, when you log in.

If you really need to have the Perl program enter the pass phrase, it might be easier to automate ssh-agent/ssh-add than ssh itself (because Net::SFTP::Foreign is using ssh).