Fast Switching kills the feature?
I have two Macs each have 2 accounts (with 2 Apple IDs), local names, etc. are identical.
If I Fast switch on each to the second user, Universal Control stops working. The only fix is to log out and log back in as the second ID. Cumbersome at a minimum using a combination of Screen Sharing since I have ONLY one Keyboard / Mouse in the Office.
I explicitly turned on Auto-Reconnect. All works OK as long as I am NOT signed in to another account on the either Mac.
iMac 24″, macOS 12.4