Can you give some more details? I have a few old laptops which I can re-purpose for this.

Place the laptop behind/below the TV, hook it up via HDMI, install whatever software you want on it (I use plain linux and VLC, but you can install Jellyfin and use the web interface if you want to), use a bluetooth keyboard/mouse combo to control it. You can enable USB wakeup if you want to minimize power usage, but you have to make sure the keyboard is plugged into a USB port that's powered when shutdown then (if that's even possible given your config).

I had an Asus TP500Ln that I only just retried, it lasted me 10 years as a TV box, always more powerful than fire sticks/actual tv boxes.

Replaced it recently with a 4 year old laptop.

I simply install Ubuntu, plug in the TV through HDMI and keep the charger plugged in all the time.

Then I can install stremio, Kodi and any other streaming apps I like. Technically I could also set up some retro games.

How do you control them?

I use one of these, very convenient. You can even buy multiple of them and place them around the room. https://www.amazon.com/Logitech-Wireless-Keyboard-Touchpad-P...

All I need in a remote, though, is a direction pad and about 6 buttons: power, select, back, home, volume up & down. And those power and volume buttons need to be routed to the display (projector in my case) and sound bar respectively.

I bought an "air mouse" remote from AliExpress. There's a lot around.

On the back it has a little keyboard for typing.

You have USB receivers that respond to regular remote controls.

I would try KDE connect to do keyboard or mouse input.