I’m surprised no one has called you out. An e-bike is a motorized vehicle, you should not be in bike lanes. Just like electric scooters and such should not be on sidewalks. E-bikes trivially go 30mph and can carry substantial weight as your pointed out. May as well just let motorbikes at that point.
I don't know about Seattle, but here in Europe, when speaking of "e-bikes" people speak of a specific category that only goes up to 25 kmph (16 mph). Basically, it only goes faster than a normal bike if it's either very loaded or up a hill.
E-bikes that go faster than that are, as you suggest, treated like light motorcycles, and require all the same things: license, insurance, registration, and equipment (motorcycle helmet and gloves in the EU) and are explicitly forbidden from riding on bike lanes.
Ebikes are not motorized vehicles, at least in Seattle. An e-bike requires pedaling to control your speed (it does not have a throttle like a car or motorcycle), it is speed limited (the motor only helps until 20mph, above that you pedal to go faster).
If your vehicle has a throttle and doesn't require pedaling, or the motor provides for speeds above 20-28mph (depending on some factors), then the regulations agree with you.
A bike like the Tern HSD is not legally classified as a motorized vehicle.
