We have the same issue (Netherlands) though it is sort of condoned if you behave like an ebike (max 25, pedal only). Strange thing is the pedelecs are under the heavy moped category which must use the roads but in general is about the speed of the lighter category which can and mostly must use the cycling paths. I guess it has to do with the standardization of EU rules with the A(M) categories of driver license.

Even weirder thing is the disabled peoples mini cars must use the cycling path and park on the curb. (NOT the bigger 45kph things which look like fiat pandas in size, those are never allowed on any cycling path despite people doing so). Though I guess since you have to be disabled to get one that sort of makes sense for safety reasons.

Thank you for your perspective.

I've pondered but haven't been able to figure out the right solution to this in general, as I'd love e-bikes to displace cars as the dominant means of transport. Maybe a 3rd differentiated lane?

The closest similar vehicle I can think of is the motorized scooter (e.g. Vespa). They can't (and shouldn't) be allowed in bike lanes. But they're too slow for all but dense cities. In my region, I know famously they're the source of lots of contention on the island of Martha's Vineyard (which has few if any bike lanes).

But, in the States, most places that have dedicated bike lanes are dense cities. Vehicles can't legally or practically drive much faster than 30 MPH (~45 kph) anyway. Even as a pedal cyclist I can usually keep up with traffic. So it's largely not a problem here yet for the larger e-bikes to stay in the car lanes.

Light mopeds (L1-a) like possibly the Vespa (I’m not familiar) are actually allowed and sometimes required to use the bike lane here. My bike is classed as a heavy moped due to the increased speed limit, although it's lighter than any actual moped.

So that’s fun.