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.

Yup, this is why the ArchiveBox browser extension sends URLs to a separate server for archiving with an isolated burner profile.

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.

I know it’s a lot of work but this would be great and it may give readers a deeper understanding into security in general.

How does it save pages that are only available when you are logged in such as social networking pages?

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).

That’s a very cool solution- gives the user explicit control