The most crucial step! Enable "Wireless Debugging" on your Apple TV.
On Apple TV:
Go to Settings → Remotes and Devices → Remote Apps and Devices
Keep this interface open. Your Apple TV will automatically enter "Waiting to Pair" mode.
(A message will appear on screen: "Ready to connect using Xcode or Apple Configurator")
Do not exit this screen!
Otherwise, Xcode won't be able to detect the device.
Topic:
Developer Tools & Services
SubTopic:
Xcode