The Apple TV has a connection limit of two bluetooth devices plus it's remote.
This means you can try to connect as many devices as you want, but it will only read data from two of them.
This is a device connection limit, not a limit to the number of signals the Apple TV can receive. This means you can get around the problem by connecting devices that broadcast multiple signals on the same bluetooth channel. Examples of this the are the Tacx Neo for power and cadence and the Wahoo TICKR X for heart rate and cadence.
It is also possible to use "Bridging" devices such as the North Pole engineering CABLE and the 4iiii Viiiia heart rate strap.
If you've got Zwift installed, turning the Apple TV off and on again will fully release the bluetooth connection and allow your sensors to connect properly. For iPads and iPhones turning Bluetooth off and on again is usually enough, but a full restart may be required (The same will apply when going back to Zwift)
Disconnecting the remote won't help with the 4K Apple TV
We will not be following Zwift's example and creating a separate "Companion app" to get around this issue.