As a non-web developer, I remember years ago when disabling cookies meant only cookies -- then learning that there were other forms of persistent storage. It made me angry and I felt betrayed.

Calling all persistent storage "cookies" matches the popular understanding of what "cookie" means. I don't see the problem with accepting that and using the term accordingly.

It may not be technically correct, but this is a point where the technical distinction isn't important. If a user disables cookies, what the user is expecting is that persistent storage won't happen at all.

Renaming it to disabling "persistent storage" would be fine, too, except that it would be necessary to explain what "persistent storage" means.