If you don't mind me extending the thread.
I tried first having one user profile for apps installed from g.play and a separate one for apps from f-droid. my bank app worked, but I found this setup unpractical.
My second approach was to install g.play, f-droid and all apps in the owner profile and make them available to user profiles. I pushed my bank app together with play store and services. all have network and notification permissions, play services has unrestricted battery (I think by default), but the bank app doesn't work - no message, just the splash screen for ever.
Another difference is that in the first setup I was logged in to the google account, but not in the second (not in the user profile with the bank app)
Am I doing it wrong or is it a limitation of the integrity api?
Oh, and for example Signal works and uses google push for notifications