How did you set it up?
Can you set out of office status in the Teams web client? If the desktop client fails to set up, try signing out and then deleting all files and folders in the %appdata%\Microsoft\Teams directory to check if it works.
According to my tests, when I set the out of office status, the input box will display the status information of the other party, but the online status will still be displayed as set by the other party. For example, available is still displayed.
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