There’s a fix for it where you remove all the unlock entries in Keychain, and then re-enable it. Only thing that worked for me long term (but it did fix it 100%)
I tried this yesterday. It... helped. But what I've now found is that if I escape out of the password prompt (which will turn the screen off again) and then try to unlock it a second time, the watch unlock will be triggered. I wonder if it's something about waking from sleep. (I also wonder if it would have worked before to do the same thing, but it never occurred to me to try.)
I use most of Apple's "built in" applications like Mail, Notes, Photos, etc. with Firefox (instead of Safari) probably the only exception to that.