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Menu bar is always black in fullscreen on monterey, so they sort of gave up on it but also fixed it.
I didn't really understand what you meant by always black, but ya, it's.... always black now lmao. Guess that's one way to fix it lol.
 
First of all, I was wrong. On Big Sur 11.6.1 after a few hours glitching returned.

Second: I've insalled Monteray on my other machine.
Here is video of how full screen menu behaves in Monteray.
Well.. There is still a little flashing glitch in menu when you exit from full screen mode (right at the end of the video).
 
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