Even when I‘m logged out I expect at least information on my geographical location to seep into the archive via URLs addressing specific CDN endpoints or similar mechanisms.
You set up a chrome profile for archiving that's logged into all the sites you want to save. I recommend using burner accounts dedicated to archiving, so you'd have to add them to any private pages/groups you want to archive.
It is possible to use your main account for archiving but there are security risks (you cant share the snapshots without leaking session headers).
I should write a full article on the security implications at some point, there aren't many good top-down explanations of why this is a hard problem.