as a compliment to my question. A couple years ago, there was a talk https://developer.apple.com/wwdc21/10003 that mentioned sharing the OAuth token with Synced Keychain Items.
That implies sharing the OAuth token, which I cannot do, but also has the effect (depending on the implementation) that if you log in on iOS, you will be logged in on the iPad and Mac if the app is present in those platforms, the same goes with log out.
Also, some of our users actually share Apple ID, which caused some issues for those users as well