Hello whitepaper,
Thank you for reaching out to Apple Support Communities, and we'll be happy to help in any way we can. We understand you have questions about the Bluetooth connection limit of Apple TV. You can find this information under the section of this article titled "Use more than one Bluetooth accessory": Use Bluetooth accessories with your Apple TV
"Your Apple TV 4K or Apple TV HD can support several Bluetooth accessories simultaneously, up to this many:
- One Siri Remote or Apple TV Remote*
- One Bluetooth keyboard
- Four MFi (Made for iOS) Bluetooth controllers (Unless you also connect a Bluetooth audio accessory. If so, you can connect only one MFi controller).
You might be able to pair more accessories, but at some point you may need to unpair others to allow for new ones. "
We hope this helps.
Cheers!