Apple mail also will NOT display recd emails....I went to library and deleted many things associated with the mail...com.apple.mail et al...........Nothing worked.
I wouldn't think that mucking around in your Library deleting items would be the best way to solve your issues. How about deleting the account that isn't working and setting it up again? How about reinstalling the OS.
You could try explain what specific trouble shooting steps you've taken to see if we can help.
For me, when I am on my 2017 MBP, if I receive an iMessage I get a notification on the MBP but my phone screen will not auto turn on to show it. If I turn on the sceen on my iPhone, I'll see it displayed in the lock screen.
With text messages, they don't even appear on the Mac iMessage anymore. But same issue when my phone is nearby, screen doesn't auto turn on showing the notification.