how do I respond using the apple relay email

I have had some confusion and different experiences, too. I notice that some apps actually let me use Sign In with Apple even if my account has already been created using another email address of mine (in this case it is my Outlook email). I also wonder if it has to due with having listed this email for use with FaceTime calling and iMessage, almost as if it were acting like an alias with Microsoft email accounts? Anyone else notice this?

You can't. Per Apple, this address can only receive email, you can't send email from this domain.