All this notifications above was when leave phone alone for a awhile. Of course they need to set to "not battery optimized".Google Play services is used for push messages if the apps are in the background. Most apps can receive push messages themselves when in the foreground.
I can't exclude that some apps will not work, but I don't need pushs from most of the apps.
I was thinking play services are required for many more things, so as location. But I just test the Bahn-App, that uses my current position. But due to missing connection of playservices I assume this position is not transferred to google. App just doesn't show the map - but this I can live with.