Wireless adapter for a wired controller

My kid has an aftermarket wired controller (due to him tearing up my OE controllers). The USB C cord is removable so that you can use a longer cable, etc.

I am trying to find either a compatible Bluetooth transmitter that will plug into the USB C on the controller and allow it to connect to the Xbox wirelessly, or a transmitter/receiver combo if it cannot connect to the integrated Bluetooth.

Does this exist? It would need to have a battery pack built in, since the wired controller has no other battery source.