In Germany, that’s not the case. What’s frequently allowed outside villages (but need explicit permission!) are mofas which are gas-powered vehicles which have a max speed of 25 km/h. The Netherlands are more permissive here but they do have far, far better cycleways.
Sorry, I’ve misunderstood.
Yet, there may be bike lanes, especially fast tracks, where S-pedelecs are explicitly allowed.
https://wattmoves.de/s-pedelecs-endlich-auf-radwegen-hier-ist-es-erlaubt/213234/
AfaIk, Mofas don’t need explicit permission on bike lanes out of town (§ 2 Abs. 4 StVO), but are explicitly prohibited sometimes *“keine Mofas”.
In town, the use of bike lanes with Mofas or pedelecs “E-Bikes” may be permitted if explicitly stated with an extra sign.
Which is actually a really crap regulation as each city has to check all of their bicycle paths and allow S-Pedelecs. Which means that there are many cities which are simply not doing that.
Many/most urban city paths in Germany are already too crowded for S-Pedelecs which go at 45 km/h.
For example, you would need to be able to safely overtake a slower bicycle which on most German bike lanes is not safely possible. And of course, it is a different thing for Netherlands bike infrastructure - but you also have much denser bike traffic there.
The problem here is, that at least in Germany S-Pedelecs are not allowed on bicycle paths at all. Which makes city driving a nightmare and is also preventing S-Pedelecs on many other paths. Around here there are many paths through nature reserves and woodland, where it totally makes sense that motorcycles are banned, but since S-Pedelecs fall into that category, you are screwed.
A regulation like “feel free to drive there, but do not even think about going faster than 25km/h” could work.
The regulation is more ar less only intended for high speed tracks ("Radschnellwege") where it is sometimes suitable to allow 45 km/h fast bikes or bike streets (“Fahrradstraßen”) where the s-pelelecs then would have to obey to the 30 km/h limit, not for each and every small narrow bike lane.