Thank you. This information was very helpful.
I think I understand more of what is happening now. It appears that something is automatically switching the profile at times - probably things that want to use the microphone switch to the “Headset Head Unit” profile, and then mostly switch back to “High Fidelity Playback” when they are done.
It seems like something got it stuck on “High Fidelity Playback”, so the microphone would not work. It almost seems like me manually switching it once got it un-stuck. I will need to do more testing, but I think it is back to working like before.
Also, I think this explains why, for about a year now, after exiting a meeting, occasionally the audio (for music) sounded really bad. I guess it was getting stuck on “Headset Head Unit” (or Teams or Zoom was not letting go of the microphone).
Now that I have a better idea what is going on, I think I can “fix” it when needed (without resorting to reboot).