Universal Control Stopped Working

I got a new 24" iMac about two weeks ago, and discovered quite by accident that "Universal Control" just worked - it was SWEET! As one is a personal computer and the other is work, the keyboard and mouse stuff was quite useful, as was drag and drop between computers. Loved it.

Until a few days ago it just stopped working. I can't figure out why. I've googled around for how to fix that, and I can't find anything that helps me get them going. Things that have already been verified and or tried:

1) Both computers logged into same iCloud account.

2) Both have all three options turned on in the Settings | Displays | Universal Control area.

3) Both can see each other as I can airdrop to each other

4) If I use the "Add display" option in the Displays area, both computers can mirror onto the other, so they know they're there.

5) I've tried turning all three UC options off, rebooting both, then turning back on, no change.

6) WiFi & Bluetooth are on for both machines

7) They're about one foot from each other, so it's NOT a space issue.

8) Handoff is turned ON on both machines, but I've noticed cut/paste from the other machines isn't working, either.

9) Both machines can use UC on my iPad, just not with each other now.

10) Renaming the Macs - saw that in someone else's post.

11) And of course, both have been rebooted multiple times - don't suggest that, I wouldn't be posting this if it were as simple as "reboot it".

The only thing that I can think of that I changed was at one point on the main 27" iMac, I accidentally logged out of FaceTime, but immediately logged back in. That's the only change I've made to either that I'm aware of.

I'm at a loss as to why UC is no longer working for me on these two computers, and I'd really like to get it back. Suggestions?

iMac (Retina 5K, 27-inch, 2019) - Monterey 12.5

iMac (24-inch, M1, 2021) - Monterey 12.5