reasonably important, if you're never connecting your lg tv to any network, and just connecting it to an AppleTV or something and letting HDMI-CEC control it so you never even see their OS.
Exactly this. And with an Apple TV 4K Ethernet, you've got a bonus Thread border router for smart home devices. I actually didn't even realize that initially, but was very pleased when I found IKEAs latest round of Matter over Thread devices paired nicely with it and my existing Home Assistant + Hue setup.
And if you install Tailscale you can even use it as an exit node to surf from home when you're traveling.
I would suggest a mini-PC running Linux and Plasma Bigscreen instead of an AppleTV if you want something 100% private and user-controlled.
Do you recommend any specific distro for this?
Arch or Fedora, because you want a very recent KDE version.
Unless you're using streaming services like Netflix, in which case you're stuck with 720p because of widevine.
my priority for a TV isn't privacy or user control, it's minimizing annoyance. and appletv, roku, or similar streaming boxes delivers that best.