I saw your Apple Support Communities post (“Broken Matter Mesh - Apple TV fails in role as gateway”) and your description sounds very similar to an issue I chased for weeks with Matter over Thread devices and Apple TV acting as the hub/border router.
In my case, the Apple TV would appear in Home as the connected hub, but the Matter/Thread side would either not show up reliably or would flap (devices would go No Response, automations would stop, and sometimes it looked like there was no border router at all). I eventually found the root cause was a VPN on the Apple TV combined with Ethernet. Once I removed that variable, everything immediately stabilized.
Here are a couple concrete tests that were decisive for me and might help you isolate whether something similar is happening:
1. If you have any VPN app or profile on the Apple TV (NordVPN in my case), disable it completely as a test.
• With VPN enabled and Apple TV on Ethernet, my Thread/Matter network would not properly form.
• Turning the VPN off restored the border router role and devices began working again.
2. If you want to keep VPN enabled, try switching the Apple TV from Ethernet to Wi-Fi (same LAN).
• In my setup, Apple TV on Wi-Fi stayed stable even with VPN enabled, while Apple TV on Ethernet did not.
• This suggests some interaction between the Apple TV VPN/tunneling behavior and local LAN discovery/routing (mDNS/Bonjour/multicast), especially on the Ethernet interface.
3. If you have only one hub, consider temporarily making sure the Apple TV is the only candidate hub while testing.
• Unplug other Apple TVs/HomePods during the test window so you can see clearly whether the Apple TV becomes the border router and stays that way.
4. Router-side quick checks that improved stability (not the root cause for me, but worth doing once):
• Disable QoS.
• Use WPA2-only on 2.4 GHz (some IoT devices behave better).
• Fix 2.4 GHz channel/width to 20 MHz and avoid Auto.
• Reserve a stable IP (DHCP reservation) for the Apple TV.
If your symptoms are that Home sees the Apple TV, but Matter never shows a gateway/border router, the VPN/Ethernet variable is a surprisingly common and easy thing to rule out before deeper resets.
If you share whether you run any VPN on the Apple TV (or at the router), and whether your Apple TV is on Ethernet vs Wi-Fi, I can tell you exactly what change fixed it for me and what the expected behavior should look like after.