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.