At least in germany, E-Bikes are easy. They're the same as bikes. They can be used anywhere except for sidewalks/pedestrianized areas without explicit "Fahrrad Frei" signs, Autobahns and roads with bike ways adjacent to them with a bikeway sign. They follow normal (car) traffic lights, except for when there are traffic lights with bikes. One Way streets are only allowed if there is a "Fahrrad Frei" sign.
E-Scooters are much more complicated. They have to use bikelanes (even if their usage is not required for bikes) and can't use "Fahrrad Frei" sidewalks, but can use "Fahrrad Frei" one-way streets. They're also not allowed to use ways blocked for motorized traffic, which is usually another way in germany to declare mixed use pedestrian/cycle streets. There are also a few other exceptions, which are even more complex. If you just pretend to be a bike, there are few to no issues with other people and even police [1].
[1]: Except for large, pedestrianized areas allowed for bikes, where police are sometimes on the lookout for E-Scooter users, due to the bad experiences with rentals.