English has the peculiarity of having two variants of the same word: “gender” and “genre” with slightly different meanings.
You could lean on it and go with genre. But just changing the word is unlikely to help much, the concept itself is deeply associated with genitalia in English culture, you’d still need to explain it.
This sounds like some silly bug in libinput.
There’s nothing in wayland that would care about whether a mouse was connected wirelessly, but libinput may not be detecting it properly when wired. I’d try reporting it, the fix is likely to be trivial.