Broken Matter Mesh - Apple TV fails in role as gateway

My Matter mesh is broken. No amount of resets will allow my (new) Apple TV to function or show as active on Matter. I have disconnected all Apple TV's and Homepods and deleted my home in the app. Even creating a new home and attempting to use one Apple TV as a gateway has failed. Home sees the device but Matter never shows up at all. I think Apple needs to reset my mesh, but nobody from Apple support can even understand the problem or refer me to the Homekit technical team.