It’s not exactly clear what the main goal is here and it sounds like a bad idea on first glance after reading your last paragraph. But it sounds like you might be looking for mandatory profiles.
https://learn.microsoft.com/en-us/windows/client-management/client-tools/mandatory-user-profile
But now that I read it again I think you might be conflating users/profiles with sessions. In which case no, this is neither possible nor a good idea. But it still might be okay with mandatory profiles if the device and app works the same from multiple sessions.
Anyway, you might get better answers if you state the full problem, including details on software and device, not just your proposed solution.
Lol Microsoft is not even close to a walled garden. This is just them removing the password manager feature that nobody used from their authenticator app.