Having the same issues with the apple mail app using exchange. The mail app shows as an alert but when I open the app it shows nothing new is in the inbox. Recently timed it and mine is taking 6-10 seconds for the email to be visible in the inbox. Then takes another 3 to 5 seconds seconds to show as read or delete once delete it hit.
I also get anywhere from 150 to 400+ emails a day. This slow down is extensive and if not fixed soon the phone will Unfortunately be returned because right now it is not even a good paper weight. Battery life is great. Other features are great but can’t afford the wasted time waiting on this “pro version” phone to load emails. Should have definitely delayed release of the phones and iOS 13 until they were at least somewhat stable and running smoothly. As my username states I am very disappointed in the phones software. The phone has many great features but it is only as good at the software running it unfortunately.
How about a true fix tomorrow Apple?