Why does Universal Control with linked keyboard and mouse need wifi?

I have two Macs. Both Macs have System Preferences > General > "Allow Handoff between this Mac and your iCoud devices" turned on. And both Macs have Bluetooth turned on. Also, in System Preferences > Displays > Universal Control > all the options are turned on.

Mac #1 is connected via Ethernet with wifi turned on but not connected to any network. The wifi menu bar icon is gray. In System Preferences > Network > Wi-Fi the Network Name is gray and says "No network selected". The internet connection is via Ethernet. In System Preferences > Network, Ethernet is at the top of the list of networks and it says "Connected".

Mac #2 is connected to the internet via wifi to a network like normal.

In the above configuration, Universal Control works for the two displays with linked keyboard and mouse. I can push the pointer to the edge of the screen and then control the other Mac.

But, if I turn off wifi on Mac #1, it doesn't work. Other aspects of Handoff work, and screen mirroring will work, but not linked keyboard and mouse.

Why?

Why is wifi needed on Mac #?

The wifi on Mac #1 isn't doing anything, is it? How can the wifi do anything when it's not connected to a network?

Is macOS using wifi to transfer data between the Macs directly even though there's no indication of that? When the wifi on Mac #2 is already connected to a router, how could it also be directly connected to Mac #1?

Or, is wifi required for some other reason?

I'm just curious. I can leave the wifi on. It's not causing a problem other than it confuses me.