You have a few options, but almost all of them are from 3rd party companies. Xbox sells a black wireless headset for the 360, it looks like a simple hands free kit for a cellphone that you stick in your ear. It’s only one sided. so you don't have

Connect an Xbox Controller to Shadow – Shadow - Support (EN) Plug the Xbox controller into a blue USB 3.0 port, if possible. Some Xbox controller functionality, such as vibration, may not be available on USB 2.0. Mobile devices may require Bluetooth setup or a USB On-The-Go (OTG) cable. To use a wireless adaptor, see Microsoft's article Set up the Xbox Wireless … Connect Xbox 360 Wireless Receiver to Windows 10 - YouTube Jul 29, 2015

Mar 31, 2020

How to Fix Common Xbox 360 Wireless Networking Problems May 08, 2020

How To Use an Xbox 360 Wireless Controller With Your Mac

All you need to get started is a wireless access point and an Xbox 360 wireless networking adapter. You won’t be able to connect to Xbox Live unless you have a high-speed Internet connection, such as a cable or other broadband system. Turn off all your network equipment (modem and router) as well as the Xbox 360.