It seems that for me Apple tried to solve a potential problem and instead created a bigger one.
I had been using notifications with Messages and all of a sudden the notifications stopped. Like many others I started looking for a solution but was getting nowhere. By accident I decided to look on the notifications list on the menu bar and right there was the answer.
I recently got a new HDMI monitor for my Mac Mini. I connected a second TV / Monitor to the display port. Apple automatically assumed that I wanted this second monitor mirrored and I am guessing Apple's logical assumption is that you are using it for a presentation. When it does that, it chooses to disable notifications by turning on Do Not Disturb. When you go to the notification list, that option does not appear immediately but if you scroll backwards on the notification list you will see a Do Not Disturb On / Off switch.
Turning that off did not make it work immediately. I had to restart the Messages App.
It could have been implemented more effectively and elegantly.
Unfortunately this took a significant amount of time to figure out. It may be the solution for a lot of others I hope.