Additional features, settings, or issues not covered by specific Microsoft Teams categories
I had the same issue and found out it is an issue with your status under your outlook calendar. I have included a screenshot. You need to make sure the status on the event is set to "Free", instead of "Away", otherwise your global status in Teams will be set to "Out of Office" and cannot be changed.
Hope this helps.
Reposting this because this has worked for me and still works.