Thanks for your reaction. I'm affraid nothing of your suggestions make any difference. I have tried everything, even tried Safety Mode, but it stays broken.
I get NO audible notifications NOR on screen notifications from Calendar activities, NOR from any other app. This has all started after installing macOS Sonoma 14.0.
Mind you: I did NOT change anything when I installed Sonoma.
Visual notifications DO appear in the Notifications Centre, but I have to click first on the date/clock symbol on the upper right side in the menu bar.
So I think something is really broken. The abnormal behaviour of the Notification Centre is definitely NOT any kind of wrong setting, as your reply suggests.
By the way, since a year or two I also do NOT get any audible notification when a new E-mail comes in either. Exception: I DO hear a sound when the screensaver is running. So this Mail issue already existed long before installing Sonoma.
Regards.