Extension of point 4 - The notifications on some apps are only received when I unlock the phone or put it on charge e.g. Gmail, Messenger (from the automatically closed thread https://zentalk.asus.com/t5/zenfone-9/huge-problem-with-notifications/m-p/...
I have exactly the same problem as you and it's very frustrating. ASUS - do you have a solution for this problem? I checked other topics and more users report this problem.