I recently set up LineageOS on my rpi4 for this. With that setup, I think you'd be able to use the Android version of Moonlight. I haven't used Moonlight before though, so not sure how good of an experience that is on Android. Since the official images didn't support Android TV, I ended up using this version. Performance is a little slow in the menus (and very slow in the Twitch app, but that's also true on the fire stick). I'll probably give rpi5 a shot at some point in the near future to see if that offers better performance.

Bluetooth game controller works quite well (a little too well, the box notifies me when controllers are trying to sync), and works with apps like RetroArch and Jellyfin. I think it's supposed to support AirPlay or whatever the Android equivalent is too, but I haven't tried that. I also had to install gapps to sign into YouTube, but most other streaming apps I tried worked without it. Some of them require specific Android TV devices though, so a 3rd party app store or side loading may be needed for some of them.

I originally wanted to use Plasma Bigscreen with Waydroid, but I ran into the same problem of not being able to find an Android TV image. I did try building it myself, but that was taking too long so I eventually gave up.