I may have fixed it, but it has only been 2 days since I tried the following:
Reset the device to Miui 13 - had a lot of issues, I likely did something by not formatting first with TWRP. So I gave that up and re-installed MIUI 14 via Fastboot.
This time I set it up as a fresh install, did not restore from Google or from another device. 100% clean install. I also did not do Face Unlock.
So far, that along with setting the right apps to auto start and to turn off battery saver... I have not been having issues.
I have not had any apps not give me notifications so long as they were set to auto start, locked in memory, and turned off battery saver.
We'll see tomorrow when I go to work and tend to get a lot more emails and thus more opportunities for missed notifications.