GOS-customer This indicates it is not services problem, but OS
It might be as well an app issue.
Among general and broad suggestions, you can try to uninstall and reinstall the app.
Also, make sure that the app has the notification permission granted, which is not following the settings inside the app.
If notification permission is granted, check what notifications the app is allowed to show, make sure that new emails notification is on.
I would say that if all the other apps can show notifications fine, the error shouldn't be in the OS.
Also, I personally prefer Tuta over Proton, and I can tell you I receive notifications even without Play Services, sometimes with some short delays.