My TVs are on the IoT network so that I can control them from Home Assistant, but they're blocked from accessing the internet.

DNS lookups are redirected or blocked (53 redirected to my local DNS resolver, 853 blocked), and DoH is blocked as best effort though it's hard to block HTTP DNS traffic, which again is why the devices are blocked in the firewall.

All streaming is done via AppleTV, which is a platform I trust infinitely more than LG/Samsung/whatever.

All of your blocking still doesn't change the fact that your LG TV is actively trying to scan your local hardware, gathering IP-addresses of devices, wi-fi names and signal strengths, creating digital finger prints of the audio and video projected on your screen, recording audio through the internal microphone, even when the TV is in standby or without an internet connection, saving the collected data locally and uploading to LG Ad Solutions as soon as the TV is connected to the internet.

If you're streaming via AppleTV, why do you need to give the TV itself access to the network?

And then your neighbor spins up an unprotected network or something like xfinity which they could have a deal with and it connects there and phones home anyways.