Both of these are true in this situation described in the OP.
".. An adjuster says that e-bikes with a throttle are considered a motorized vehicle and there is an exception for those in my policy. I did some quick research and some articles saying that e-bikes are treated as usual bikes by California law."
I will take the second part first. Class 1, 2 & 3 eBikes are just bikes in California and not motor vehicles. The problem here is that yours did not fit into those classes, so it is not a bike in-law. Your conveyance was designed so that it could be operated for example with a broken or missing chain or broken or missing pedals or gears, at speeds over 20Mph. In other words, it could be operated without pedal power at those higher speeds. To quote the policy exclusion, a conveyance "
that is designed to be operated solely by use of the power from the electrical system.." The problem is that the "bike" was left unlocked. To quote you, "class 2 by default with unlock." It is the unlock that turned it into a motor vehicle, letting the insurance company off the hook. I am sorry for your loss.