I plugged in my Logitech headset and happened to be poking at USB HID stuff so I noticed that my mouse driver recognised my headset as a mouse…
So… that got me thinking about the dongle. Of the two compatible dongles, it's the "basic" version; it is exclusively for the headset audio. There's another version which is also a "Unifying Receiver". For a moment we were speculating that maybe it's literally the same hardware and so reporting as a mouse, but… they're different sizes.
Okay, so, to my favourite teardown without a spudger resource, fccid.io.