The MacBook version of the mount, will only fit the very narrow edge of a MacBook Display.
A monitor/TV mount version has a folding, adjustable, prop up leg that braces against the back of the monitor.
You can use a monitor mount version on a MacBook but not a MacBook version on a monitor/TV.
I use an excellent, sturdy, all metal, strong magnet monitor/TV mount, that I got from Amazon for less than $CAD 20.
Search Amazon for ASIN (product number) B0BZP93WPY
I have found FaceTime on Apple TV to be a little buggy. Both times I have tried it did not work right away, and the rest of the group immediately lost interest. That was with an iPhone 13 Pro Max, and Apple TV 4K 2nd generation connected via ethernet to my home LAN. Strong, fast, WiFi signal, on high end WiFi router, in the same room.