Cool videos, thanks! The driver shown in the first video is indeed a piezoelectric actuator, but not the type Canon uses in their lenses. The driver shown in the second video is probably related to Canon's Nano USM.

Do companies like Canon manufacture these motors or actuators themselves? Or is there some other company that specializes in this sort of thing?

As far as I know, Canon controls a large part of the supply chain and has numerous factories to manufacture quality-critical parts (especially their lenses, zoom mechanisms, and barrels) themselves. But there are numerous components that are more efficient to obtain from third parties, such as microchips. I am not sure about the motors and actuators, though.