Homekit hub

I just replied to a related post where I suggested assigning a static IP to the ATV in the router settings. It seems that with the latest tvOS some ATVs are having difficulty connecting to the network.

All routers are different, and their configurations may look quite different from one model to the next. That makes it near impossible to give a guide by description. Consult your manual or contact the manufacturer.

I have remembered that I encountered a similar issue (unable to access Homekit devices remotely) when I was staying at an AirBNB. I set up a spare ATV there and, even though it wasn't acting as a Home Hub in that apartment, I was unable to access my real home whenever my iOS devices were connected to the apartment wifi. As it happens my real Home Hub ATV is connected by ethernet. I didn't think of trying connecting it by wifi but it might have worked then, as you have found.

So... it could be a bug in the Homekit software.

You answered your own question, they work when connected to your home Wi-Fi network.

Set up your HomePod, Apple TV, or iPad as a home hub - Apple Support

Ethernet (cable) is fine. It is the home network with wifi/ethernet that is needed. I use ethernet for my ATV and wifi gor Jomepids & iPad. They can all work as Jone Hubs.

Ah - it is likely your ATV has a defective ethernet port. Happened to me a few years ago. I had to just use wifi.

Verify that your router bridges the wireless and wired into one logical network. That is needed for devices on one part to communicate with devices on the other part.