Selfhosted

The main issue for me is not finding a device to play content, but a dumb screen that is not a potatoe. A 4k HDR OLED Screen without any smart features is basically nowhere to be found

As others have suggested, OSMC is OK, but personally I prefer having Android so that I can use SmarttubeNext and access native apps for stuff like Jellyfin, Dropout, Nebula, etc. For years I played with various Linux options, but in the end I ditched it all for an Nvidia Shield and I couldn't be happier with the results.

have a look at OSMC, you write it to the Pi SD card and it gives you Kodi all setup and ready use. you can even use your TV remote to control it

I literally have a rpi4 and just put libreELEC on it

I find having the full OS is useful, and this KDE environment proves great https://plasma-bigscreen.org/

I have been meaning to give this a try. https://osmc.tv/store/

As others are saying, OSMC might work. Most difficult part is making it so that the TV turns on when you turn on the computer since ARC isn't a thing for most computers.

I ended up giving up on OSMC and bought an Apple TV since nothing else got the "wife approval" factor. It's better than Google getting my data, has a Plex client, and let's me stream my Steam library.

If Android is okay, I'd recommend the ONN 4K Pro player from Walmart (if located in the U.S.) with some privacy caveats:

• Do as little with Google: Make a throwaway login if Google requires one to get the device started up. Try to avoid Google Play Store as much as possible. If privacy from Google isn't a concern, feel free to use your Google account to download apps from the Google Play Store.
• Learn how to sideload apps: There are multiple ways to do this, like a USB drive or FTP server.
• Pick an alternate launcher: This will replace the default Android TV OS UI with one that has much more flexability and no ads. FLauncher and Projectivity are ones that I recommend to friends.

The final product is a modern streaming device with much more flexability than any other store-bought device. Building a HTPC with Linux is probably the true self hosted option. Personally, I'm able to afford some privacy sacrifices with Google for something that "just works."

It's been years since I've shopped for a TV, but... can't you just not connect it to the internet? I have a little microPC running Linux connected to our TV; it's smarter than any other TV I've seen, but the TV itself is stupid.

Why can't someone just get a smart TV and just never let it get online?

I mean, sure, if I had my 'druthers, I wouldn't be paying for features I don't use, but if it's literally impossible to buy dumb TVs, what's the issue?

LibreELEC

Fwiw - I have both an LG C2 and a newer Samsung QLED. Neither have ever been connected to the internet, never pester me to connect, and the both turn on right to to my Apple TV

Currently I'm working on a Plasma Bigscreen build that still gives some privacy and 1080p Netflix/Disney+/Crunchyroll etc by using extensions/WebApps and getting S-Tube and other android apps (including tv web browser) via Waydroid + Flauncher, all controllable through a simple IR controller.

If you pm me I'll set it as a reminder for when I finish to share the package. It's designed for an Odroid C4.

As for dumb tvs or more privacy friendly tvs, you can find them if you know where to look. Here's some options from LG:

https://www.lg.com/us/business/digital-signage

They had a dumb 65" 4k OLED too but it's currently out of stock.

The option(s) other commenters gave are great! But just to give you more options, I'll give you a few additional ideas.

1. KDE Connect: You can still use a normal desktop (preferably KDE or Gnome), set your display scale to 150+%, and then use your phone remotely to control the cursor, media playback, and more.
2. Bazzite: often used to replace SteamOS, it also boots into Steam big picture mode by default, where you can set applications in the start menu. It has a nice console-like interface, and you don't have to maintain anything, e.g. updating. It also supports Waydroid and webapps by default.
3. An old laptop or mini-PC with Bluefin or Aurora. They are basically like Bazzite, but without gaming stuff. You can set the display scale to 200% and enjoy a worry-free experience. Optionally, you can install Phosh or Plasma Mobile on top, which is made for mobile devices.

You could install android on something, and run one of the open source TV launchers

OS ≠ user interface.

Use whatever OS that runs Kodi or some other user interface the best (with privacy also being considered to be best).