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I recently had an issue accessing Microsoft Teams using a web browser even after logging into Microsoft 365. I could get to just about everything else but Teams, which always threw up a login dialog as shown above.
The issue turned out to be the time of the local device which hadn’t updated for some reason after a change to daylight savings time. Thus, the local devices (Windows 11) for some reason was one hour ahead. After changing this so the workstation had the correct time, everything worked as expected.
Hopefully,this helps someone else who is searching for this strange one.