Zeuser -
in the USA the federal law does not supersede state law in regards to what is an electric bike.
disclaimer:Ask a lawyer if you want the definitive answer, but as far as i know
the state decides what is an electric bike for the purposes of road-going vehicles, licensing & insurance.
the federal law decides what is an electric bike for the purposes of "is this product regulated by consumer product safety laws, or by highway transportation safety laws?"
In other words, it could be that you have a motorcycle as far as the "is this allowed on streets/what lights does it need/what insurance" question is concerned, but an e-bike as far as the "who regulates new-product safety features on this machine". It could also be the other way around.
The state law side of things more often applies to individual riders and the federal law side of things mostly applies to dealers/manufacturers.