In response to my question above, there were many replies. There was a complex "12 step program" from stoska992. Also, jd2020 replied, and had many more steps, part of which included stoska992's program.
I looked at these, and decided I was going to stay with simply entering the manual unlocking of my iMac. I'd already tried so many alternatives before approaching "The Community." These procedures just seemed to be too much of an additional time sink to be worth even trying. I had resigned myself to having to enter the unlock code manually for ever.
As a throw-away action, I decided to power down the watch; leave it for some minutes before powering up again.
Lo-and-behold: that did the trick! It's working again on my system - no guarantees for others, but just maybe ....
Thanks to all who took the trouble to provide us with their solutions.