I'd guess, it's the authtoken cookie, since that has the right kind of expiry date for me and, well, makes sense from an OIDC perspective.

I might see, though, if the suggestion from @AlecSadler@lemmy.dbzer0.com maybe works. The Outlook webpage also redirects to outlook.cloud.microsoft since like, yesterday, which might've also unfucked things somehow? At least, I didn't get the logout loop, when I did try to test Alec's method just now.