In my state we classify e-bikes into 3 categories. Categories 1 and 2 are allowed on MUP and other places regular bikes are allowed (sidewalks provided there's no safe alternative in the road). Cat 3 bikes (those with motors that provide assistance beyond 20 and up to 28mph while pedaling) are not allowed on MUP's even though they're still classified as an e-bike.
All bikes, 2 and 3 wheeled with a motor less than 750 watts are considered e bikes. Class one is a pedal assisted bike that provides assistance up to but not past 20mph. Class 2 are bikes that propel the vehicle up to 20mph but not beyond and they do not have to have pedals. For instance those lime scooters people zip around town on. Since they don't go over 20mph and have 2 wheels they're allowed on MUPS.
I'm guessing your state has some sort of regulation and laws just like this.
Stay safe out there.