You do not need a driver’s license to operate an electric bike. Class 1, 2, and 3 bikes are street legal and do not require a driver’s license. Of course, when more bikers hit the road, the laws may change.
You don’t have to worry about inspecting or registering your e-bike in any state other than Hawaii. Of course, you should check the e-bike laws for your state before heading out on the road.