I do not use Outlook so for me deleting that app was not an issue.
I also had Microsoft Office installed with outlook and even tho I was not using outlook, as soon as I deleted Outlook (I kept Word and Excel installed) my Mail notifications started to work. After about 3 hours today with Mac Support we stumbled on something by accident and I have had zero issues now since. I would get the badge in the dock, but no notification of any type on my screen, or in the Notification Center and there would be NO notification sound either.
I was not receiving ANY Apple Mail notifications at all. Not sure if this will help you/anyone but I was having this issue since I purchased the new MacBook with the M1 chip.
