If you use Teams, you probably already know that you can set your Out of Office using the Teams client (see https://blog.hametbenoit.info/2021/05/13/teams-you-can-now-enable-your-out-of-office-from-teams/).
Unfortunately, this option was not available on Teams mobile.
Well, good news as it is now available also on the mobile application.
To do so, open the status menu to select Out of office
Then you can set your out of office message – note: if already have one set from your Exchange mailbox, the message is automatically reused – and the activation/deactivation dates