Ignore passwords from Apple Passwords menu bar companion app

I've started using the new Apple Passwords app. I was able to add the app itself to the exclude list so that Paste ignores it, so that part is working as expected. However, passwords that I copy from the menu bar companion app still get read and copied by Paste. I tried manually adding that extension separately, but Paste doesn't add that app to its exclusion list. Please resolve this issue so that Paste doesn't copy passwords from there.