bookreader
This is not the case. Apps in other running users profiles will not be fully closed unless the system requires the memory. Can stop other user profiles running with "end session"
If you are experiencing apps closing constantly it does suggest you have apps running that have high or excessive memory usage.
Keeping 2FA codes in a different user to where you will need them is a painful way to operate. In most cases there are limited security benefits to doing this as the security boundary between user profiles is no stronger than the app sandbox. All 2FA apps will keep 2FA related data protected within their app sandbox.
Likely best to set up a 2FA app in all users where you will need to use 2FA codes