Can't unlock iMac with Apple Watch in Catalina

I assume you mean the "Cancel" on the login screen? Hitting Cancel and trying again doesn't seem to do anything for me, though. There's just a brief pause while (I presume) the iMac tried to communicate with the Watch, and then the password entry field comes up. Sigh.

Thank you. I hadn't seen that precise link but had already tried everything in that article except for re-pairing my Watch with my iPhone. Aside from being a pain, the fact that the Watch will unlock my MacBook Pro and even this iMac (when booted into Mojave) suggests to me that doing the re-pair isn't the issue, but that it's something with 10.15.2. I suppose I could try to reinstall 10.15.2 although I'm not real eager to go through that if there's a better solution out there.

So Apple Support helped me to solve the problem. Turns out there was something funky or corrupted in my network setup. They had me create a new Network Location in System Preferences, and bingo, all was well with unlocking with the Watch and all the associated Continuity/Handoff functions. And as it turns out, once I had a new Network Location, I could switch back to my old Location and it continued to work.

Reinstalling 10.15.2 didn't help.

Sure. You go into System Preferences and choose the Network preference pane. From there, click on the Location drop-down menu and select Edit Locations. Click the little "+" sign down in the lower left, give the new Location a name if you want to, then click "Done". At this point, for me two new services were created (Ethernet and WiFi) but neither was connected. Click "Apply" in the lower right and the new network services should turn green. At this point my Watch could now properly connect with the Mac, for both unlocking and for Continuity.

Hopefully this helps.