This would be a rpi or mini PC plugged in, yeah. Really it's not actually much different than Chromecast, same general ideas and technologies. It might be possible to make an open screen server that runs on Android running tv's, but deploying to those things is, to my understanding, a sort of deliberate hell orchestrated by everyone involved, from Google to the TV makers.
Generally I recommend -- like with Chromecast -- using your phone to launch and control apps, using your phone as the locus of control. Maybe having a gyro mouse or Bluetooth keyboard connected to your pi... but the originally Chromecast was input less, was a networked output. To cast a thing was just to tell the display or speaker: go to this URL. And then to have some communication channel open from your phone or casting computer to the display or speaker. Any web page can use Presentation API to start a cast, to extend itself to another device. It's amazing. https://developer.mozilla.org/en-US/docs/Web/API/Presentatio...
Under that model, there is no remote. The phone is the remote.
To run a regular TV is harder. Yeah I don't recommend trying to host a whole media system. You can run jellyfin on many TVs or maybe plex. Some rare brave souls go and build their own castles in the sky. Personally I feel strongly though that people clutching at remotes & making the tv itself the locus control are doing it wrong and that the cast model is fundamentally much better, and that the tv itself ought be a blank slate.
https://arstechnica.com/gadgets/2024/07/broken-linux-laptop-...