Managing presence indicators such as Available, Busy, or Away to reflect user availability
For me the solution was to completely remove all Teams installations via Settings - Apps - Installed apps. So remove Microsoft Teams, Teams for work and school, Teams Office integration, Teams Machine wide installer, Classic teams, etc.
Then I downloaded the latest x64 client for work and school here: https://www.microsoft.com/en-us/microsoft-teams/download-app
Installed it, and immediately it started to work.
You have Microsoft Teams version 24033.811.2738.2546. You've got the latest version. It was last updated on 14-3-2024.The client version is 49/24020205514.