I spent about 3 or 4 hours trying to solve this. This was more of an impactful bug for me than most, as I'm a senior physician and my unclear notification status was creating all sorts of problems for administrators, partners, nurses, fellows, residents, and students. Like many here, I tried turning off everything, but could never get better than "Dr Braindead Mac has notifications silenced". To further complicate the issue, I have become heavily dependent on Apple devices (TVs, laptop, home computer, work computer, iphone, ipad, watch) so I couldn't figure out what device was causing the problem. Sharing here, hopefully this will help others.
The solution was totally counterintuitive. I turned off all the Focus features on my laptop and home computers and iPad, just made these changes on my iPhone (since it was the iPhone upgrade that seemed to start all the nonsense):
First go to Settings > Focus and turn on "Share Across Devices"
Then from same tab Settings > Focus > Do Not Disturb tap "Focus Status"
On that screen, toggle "Share Focus Status" to on.
Now go back to Settings > Privacy > Focus and make sure "Shared With" Messages is toggled on. Now toggling on and off the Do Not Disturb setting will work as intended and people should not see either the "Joe Blow has notifications silenced" or "Notify anyway" warnings when the Focus is off.