I'm not using that setup, but I just don't use remote control at all. The TV control is done through the "single-button interface". I guess you could say XBox controllers are remote controls.

You need an HDMI CEC dongle or a USB remote plugged into the computer.

There's really cheap bluetooth remotes available on aliexpress, most also come with a usb dongle.

I bought one for $5 and was surprised by the quality. It has an accelerometer to control the mouse as well. Great for presentations. It's a G20S Pro BT but there were lots of other alternatives.