Mail App does not do notifications for new messages no matter what settings are
2022 MacBook Air with M2 chip running macOS Sequoia 15.6: Using default Apple Mail client to receive/ send emails on several accounts. Some use POP, some IMAP, and some are Microsoft Exchange accounts. The Mail app has major problems with handling new mail: will not show notification banners or alerts at all, will not play sounds for new messages nor for other mail actions either, sporadically can be made to show badges in the Dock icon indicating a new message is received but there does not seem to be a pattern about when that happens. Problem behavior persists when booted in Safe Mode.
In answer to the inevitable questions:
• Yes, I have gone to "System Settings" > "Notifications" and turned them ON for the Mail App, currently have it set to show Banners but have set it for Alerts at other times with no difference in behavior, "Show notifications on Lock Screen " & "Show in Notification Center" are ON for the Mail App.
• Yes, I have gone in to the Mail app, selected "Settings" > "General", have set the "New Messages Sound", and have toggled ON the option for "play sounds for other mail actions".
• No, I do not have ANY "Focus" settings turned on (and I would dearly love a way to expunge everything "Focus"-related from my computer!) I do NOT have it the computer in "Do Not Disturb" mode.
• The sound on my computer IS on and can play alerts for other apps (including Apple system Apps and third-party Apps) besides Mail without any trouble.
• I do not **believe** that I have any Accessibility settings that would block this behavior, but there are hundreds of Accessibility settings and they must ALL be set individually so I do not have the time to test each and every combination because the infinite wisdom of Apple dictates that you can not have a single, global Accessibility "kill switch" for purposes of eliminating those settings as a potential cause of troubles. Again, the fact that OTHER apps work just fine suggests that this not about a system-wide setting like Accessibility.
Background observations:
A couple months ago, I downloaded a few other mail clients apps from the Apple App store hoping to find one that will replace and improve on the default Mail app (which really does not work at all well with the Exchange email accounts!). Apparently the act of merely installing another client on my computer permanently disrupted that ability of Mail to recognize when an incoming message is new or not, and prevented it from generating the proper notifications. Some of these apps installed various Launch Daemons & other background scripts that would run even when the App had been terminated. I went to "System Preferences" > "General" > "Login Items & Extensions" and turned each of these off. Did not help.
I have now removed all of these apps from the computer (to the best of my ability, since the whole "drag it from the Application Folder to the Trash" workflow still leaves vestiges in a myriad of folders across the OS one of which could still be running somewhere, I guess???) I was briefly able to restore badges, but those turned off again eventually.