I use temporary-containers on firefox and they are a marvel for working with microsoft's stuff, which absolutely doesn't anticipate two accounts working on one browser.

Of course "open in incognito mode" works for this as well, just less automatic.

I just run completely separate browser profiles to separate work and personal stuff. And I still sometimes need private mode or a throwaway profile to get some random thing to work.

Firefox's? Yep. Edge's? Bloody hell no.