Managing personal Outlook.com account settings, security, and privacy
I was able to fix this on edge by deleting all live, msn and other related Microsoft cookies. I used Ray's solution on Chrome to do it on Edge also.
This issue came up again for me. This time the fix was to install the latest update to Windows 11, can't remember the version number but it wasn't a single patch it was one of those 22H-24 type patches (no that's not the number I don't remember the number). I usually hold off on those updates because lots of bugs are found and fixed before I actually install it on my systems. Once I ran the patch voila outlook.com magically started to work again without me changing my password or anything.