I think I found the culprit – Chrome Remote Desktop – but is there a way to fix it? Even though it's not actively running (i.e. a remote connection), I get this on the lock screen:
With the little binoculars in the top right:
When I uninstall Chrome Remote Desktop it will unlock again with the watch. I feel like perhaps I'm not doing something right because it didn't do this on Mojave.
Why is my screen being shared even when it's not active?
(Additional note: I also have Screens Connect actively running without issue -> I can still unlock the mac with the watch, and the binoculars do not appear on the lock screen. It's definitely something going on with Chrome Remote Desktop)
Best Answer
Sorry for posting a comment as an answer to the main question, but unfortunately it appears I do not have enough reputation to leave a comment.
Anyway, I just wanted to point out that there was indeed an update on Chrome RD side: to be sure, I checked current version (80.0.3987) of /Library/PrivilegedHelperTools/ChromeRemoteDesktopHost.app and went into Time Machine to compare with the version I had before a couple of days ago (78.0.3904).
Also, I remember that a few days ago that I was asked to enable some Privacy settings in the Preference Pane when the update passed -- and I did so as instructed by some Google-looking GUI that appeared at start-up. I think they were 'Accessibility' and 'Screen recording'.
Since the update, I too have been experiencing the very same symptoms: that is, unlocking with Apple Watch stopped working.
HTH
Sergio