mail banners not showing

Boot into Safe Mode according to Start up your Mac in safe mode - Apple Support and test to see if the problem persists. Reboot normally and test again.

NOTE: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

Hello Souster100,

Thank you for using Apple Support Communities. Based on your post, you aren't getting banner notifications for the Mail app on your Mac. We'll do our best to assist.

When you open System Preferences > Notifications > Mail, is there an option for the banner? If so, make sure it's selected. Do you have 'Show Previews' set to Never at the bottom? If so, you'll want to select the default option of 'when unlocked' or 'always'.

Resource: Use notifications on your Mac

In case you're having issues receiving emails, see: If you can’t receive emails in Mail on Mac

Does this help to resolve the issue?

Hoping this helps out, take care.