This is a longstanding issue and there’s not much that can be done about it… the only way to not share your email address when sending a PM by email is to remove it before sending your reply. Different email clients handle this in different ways. In gmail the email address of the person replying is not included here but in other clients it may well be.
There are these admin settings you can try:
I guess one thing we could do is obfuscate any emails shared via PM… but that would potentially cause problems in those cases when you are trying to talk to someone about email addresses!