Legal Question in Consumer Law in California

For all practical purposes they are accountable to no one.

There are also a lot of civil code sections that specifically regulate storage facilities.

Like most other businesses there are laws that govern their activities, but that does not mean there is an agency that registers or regulates them. The Secretary of State does not regulate or register any specific type of business that I know of. The SoS keeps records of corporations, LLC's, LLP's, and limited partnerships, and provides some regulation of the issuance of securities in connection with those business forms, regardless of the industry. But it does not regulate any particular industry. To my knowledge self storage businesses are only subject to general business regulations such as local business licenses, zoning, building codes, etc., that apply to all businesses.