In most jurisdictions e-bikes are motor vehicles. Frequently if they are under 1000 watts they are in a special class of motor vehicle, same as mopeds/scooters. Technically they are typically not legal to have on bike paths, as motor vehicles. But this varies by jurisdiction.
Over the 1000 watt limit (1200w or 1500w some places) they tend to be considered motorcycles and require a license and break lights at a minimum to be legal.
Basically everyone ignores this and treats them like regular manual bicycles though.
Most places have rules for ebikes with pedal assist and power below certain limit, 250W in the US, are treated the same bicycles. Throttle and more power aren't ebikes but electric mopeds.
Over the 1000 watt limit (1200w or 1500w some places) they tend to be considered motorcycles and require a license and break lights at a minimum to be legal.
Basically everyone ignores this and treats them like regular manual bicycles though.