FWIW, I went out looking for a better category (something more like "two-wheeler" but without the engine), and discovered that Wikipedia actually agrees that scooters are motorcycles.

Scooters are arguably more like traditional motorcycles than ebikes.

Reminds me of this scene from Police Academy 3: https://www.youtube.com/watch?v=cil6HFXlccw

And electric bicycle is in sense also motorcycle...