Reference: https://discussions.apple.com/thread/253467325?sortBy=best
After a million tries.... the following process worked! This is using all legitimate tools, so no drama!
To fix failed activation, and therefore restore AirPlay capability, on a Mac, install Apple Configurator 2 from the app store.
Plug in your Apple TV 3rd Gen to power and to a Mac using a micro USB cable from the Apple TV to the Mac.