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https://www.dmv.org/ca-california/other-types.php

For electric mopeds, it's based on horsepower, not engine size.

I don't think this is correct. According to that link:

A motor-driven cycle has 149cc or less engine size. CVC §405 A motor-driven cycle has to be registered and the driver must have a motorcycle license (M1).

That page indicates that you do need an M1 for motor driven cycles(less than 150cc), and an M1 or M2 for Mopeds(which is news to me).