The point is: which brands still respect user privacy? If I were to buy a new TV today, which brands-models should I prioritize? Also, are there brands-models that in which it is possible to sideload a different OS like with mobile phones (LineageOS, GrapheneOS, etc.)

An Apple TV would be the best for privacy you can easily use but not perfect. Don't use streaming services. Torrenting with a VPN would share the least data but Nuvio/Stremio wouldn't share much with adtech. Can't use those on an Apple TV without sideloading :(

Our Android TV (Sony) has an option to basically make it a dumb TV. Not sure whether that still exists. We use that + simply don't plug a network cable or set up WiFi. As long as they don't add cellular modems, this works.

I bought a projector in part because they are behind on this and only seem to have basic software