After years and multiple major releases of tvOS of troubleshooting my Wifi network, and Homekit devices, and increasing the size of the dent in my forehead, I finally figured out why my Homekit environment was so unstable. It turns out if you have an AppleTV (running 16.6 or prior as of this writing) as the active controller/hub, then everything goes nuts. Devices sporadically appear and disappear, pairing is unreliable, even Thread networks become unstable. The moment you disable AppleTVs from participating (by removing them from any Room), and a HomePod takes over, everything becomes stable. I looked around on forums, and found I am not the only one with this symptom.
Since making the change about 3 weeks ago, I have not had a single issue with my Homekit environment, nor problems with Wifi in general.