Thanks for the additional steps to try. Both devices were up to date, so I proceeded to the second step of restarting both my phone and my Apple Watch. After doing so, I tested the Breathe App and tried cover to mute so the face would stop. I set the app for 5 minutes of breathing. It worked for approximately 3 breaths after I covered it, then it stopped (both having lit face & haptics) When I tried again, it immediately interrupted the all upon using the cover to mute, as I originally reported to be the problem. Upon re-entering the app, it gives a message of “Your breathe session was interrupted.” I am getting ready to try the third step, resetting the apple watch, to see if that fixes it. I will reply with the results.
As for your question if other apps continue to work with cover to mute, I tested it using the workout app since this is another app that I would want to run silently. It appears to work correctly, meaning that when I cover the face the display turns off but the app continues to run. When I tap the face again, the display comes back on and I can see the workout is still active (time counting, heart rate monitored).