I did the same but with waydroid's android tv build. It is a bit buggy and setting it up was not easy (using adb sendkey to increase volume on first setup...) but works fine. I switched to it cuz the android tv stick we had was slow as molasses but I wanted something to replicate the ease of use of it. It even works with the remote of the stick after remapping! I installed it when it was new & had android 11, now it is 16 and I assume much better now.

https://github.com/WayDroid-ATV/waydroid-androidtv-builds/