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.
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 am not sure how, but at one point even private browser mode would still have me logged in to Entra ID. Couldn’t log out of main browser and same session would follow me to private.
