Yes, that’s basically what I was getting at. So it sounds like as long as Google knows the account emails are being forwarded to (can see the headers) there is no notion of privacy.

Is there any private way to have emails forwarded from a service like GMail to Proton? I know you could forward to an alias on the Proton account, or alternatively forward through a third party (which you would then have to also trust), but I want to hear from people who know more on the topic than me.