Parts of this twitter points might be in the next tvOS 16.4 beta, there is a thread about that
Even if its announced a day sooner, it shows it has the 3rd gen remote pairing issue addressed.
tvOS 16.3 (20K650), same build as RC

Apple Preparing to Re-Release Revamped HomeKit Architecture That Was Removed From iOS 16.2
Apple with the iOS 16.2 update introduced an updated underlying architecture for HomeKit and the Home app, but it was pulled a week after launch...

Apple with the iOS 16.2 update introduced an updated underlying architecture for HomeKit and the Home app, but it was pulled a week after launch because of bugs and installation issues. At the time, Apple said the removal was temporary and that the upgrade option would "return soon."
Other than stating that the architecture would be made available "soon," Apple has provided no timing. We are expecting an iOS 16.4 beta to follow the iOS 16.3 launch, and it is likely that the architecture update will appear in that beta. As of now, we don't know when the beta is coming, but it could be as soon as this week.