Issue

There is a bug in Teams where if you except an Out-of-Office invite from a team member, your status will show ", Out of Office". That is, if you select "Available", "Busy" or "Do not disturb", your status would be one of those appended by ", Out of Office". If "Be right back", "Appear away" or "Appear offline" are selected then it will only show "Out of Office" as the status instead.

Fix 1

You will need to change the invite from "Accepted" to "Tentative".

You can do this in "Teams: Calendar" or "Outlook: Calendar".

Select the invite.
In the pop-up, click "Change" at the bottom.
Then, click the "More Options Button (3-dots)" on the bottom right.
Select "? Tentative"
Doing this should allow you to control your status as normal.

Fix 2

Similar to the answer provided by @Alexis-NG , on the use of "Free", you can do this from Teams as well.

Go to "Teams: Calendar".

Select the invite.
In the pop-up, click "View event" (Multi-Arrow Icon).
In the Event Tab, you will see "Out of office".
Click it an change it to "Free" or "Tentative".
Your status should change immediately. If not try restarting the application.

For other solutions, you can follow the discussion: "My status is set to Out of Office and won't change".