I were stuck for a while trying to pair the thing to the other thing.
At the end, I found this post. In summary, you just have to go to "Settings" > "Remotes and Devices" > "Remote App and Devices" in order to make the Apple TV visible to Xcode. I tried this on an Apple TV 4K and Xcode 14.3 and it instantly appeared It takes quite a long time to "fetch debug symbols", but at least is paired. 🤷
You may give it a try.