We have that in Germany, 25 for regular e-bikes. Anything above requires you to register and insure your bike, you get an actual license plate and you are considered a vehicle not meant to use regular bike lanes.
Not quite. Only the motor assist has to shut off at 25 km/h. You can go as fast as you want (and your legs allow) with most e-Bikes. The ones which require a license plate are extremely rare.
Fun fact: the default speed limits of 50 in built-up areas and 100 on country roads do not apply to bicycles without license plates. Those, by law, are only for "Kraftfahrzeuge". Signposted limits on the other hand are for "Fahrzeuge aller Art", which includes bicycles and horse carriages.
Actually was once caught going 35 km/h in a 30 zone but the police (hunting speeders near a school) were more impressed than angry (mountainbike, doesn't really have the transmission for speed fastest I ever went with that thing was 38km/h on flat ground). It's downhill or race bikes where you have to start to worry.