AFAIK, there isn't any official USB protocol for this, and I think there really should be. Pairing has to be out-of-band to be properly secure against MITM attacks during pairing, and using USB would be such a simple way to achieve that.
Apple has a proprietary USB protocol for pairing its own wireless keyboards, trackpad and mouse, and Microsoft and Sony have proprietary protocols for their respective gamepads.
Recent Xbox controllers support both Bluetooth and a proprietary protocol; Microsoft sells an optional dongle to use the latter on PC.
AFAIK, PlayStation wireless controllers are Bluetooth-only, but the DualSense (PS5) controllers use some proprietary extension not supported on Windows for haptic feedback over wireless that's sent via standard audio protocols over USB.
Apple has a proprietary USB protocol for pairing its own wireless keyboards, trackpad and mouse, and Microsoft and Sony have proprietary protocols for their respective gamepads.