Arch wiki says
Both the wired and wireless (with the Xbox 360 Wireless Receiver for Windows) controllers are supported by the xpad kernel module and should work without additional packages.
I guess my question is, have you tried plugging in the receiver? You’ll need the receiver for it to work, they are 2.4Ghz not BT
I read too fast you said found the receiver, haha. Yep, supported! Hopefully plug and play 🤞