Same. And I don't use Exchange. Basically, the mailbox list doesn't update, regardless of any "Updated Just Now" message. I need to back out and go back into the mailbox for it to bother updating the display.
[doublepost=1565974195][/doublepost]When I pick my phone up, it regularly says 4G instead of WiFi, despite me being in an area with an excellent WiFi signal. It takes around 3 seconds for the awakened phone to decide to reconnect to WiFi.
This is the same as the issue I have with it continually dropping to Mobile Data when on WiFi and on a FaceTime call. I tried logging this as a Feedback, and despite the many (at the time) comments from other people with the same problem, Apple just immediately closed it with "unable to diagnose". I've logged it again. That'll learn 'em.
Im using Exchange with G Suite on an iPhone X and same behavior. Often times emails won't display. Force quit the app and the message will display. On my wife's phone (similar setup with G Suite Exchange) and last night her emails would show up in All Mail but not the unified inbox. I have a regular Gmail account and outlook.com as well. When I get up for the day Ill see notifications for emails but the new emails don't actually load into the inbox until a few seconds after opening the app.
Whatever they did with the Mail app hasn't been getting fixed, and I'd think they'd be showing better progress by now. About a month to go until they have to really start loading iOS 13 onto new devices, and we've been at this for a few months now with no real improvement.