With my (2018) MacBook Pro in clamshell mode connected to an external monitor (no hub) and a Magic Keyboard & Magic Mouse connected to the MacBook via Bluetooth, I can use Universal Control over to a gen7 iPad either side of the MacBook. Whether the iPad is connected to the Mac via cable (for charging and/or syncing) doesn't matter. Not does it matter whether the MacBook is open or shut. Of course, if it's open I also get to use its keyboard & trackpad just as well as with the Bluetooth'ed keyboard & mouse.
I surely don't see anything in wifi.log saying anything about UniversalControl at all. Occasionally I do get a log entry with the "ERROR:" tag, but those are only ever about rapportd or sharingd "not entitled for com.apple.wifi.join_history". Start by going to the very top right of this web page you're reading, and click on "Get Support".
I have no ideal why you're getting all those "ERROR: Universal Control [...] not entitled for comp.apple.wifi.events [...] but that doesn't look good at all. I really recommend that you talk to Apple Support directly.