Reminds me of this more abstract perspective: you can draw an analogy between working the filesystem, and programming languages working with memory.
Yeah I really bumped on this. A cache is absolutely state. It is sufficient to say "a referentially transparent cache is a technique to store state while avoiding most of the drawbacks typical to storing state". This is already a big accomplishment! No need to also redefine the word "state" to make the technique seem even more magical than it is.
That said, you are right that as a user of the system, that statefulness is abstracted from you and you don't have to worry about it (until some subtle caching bugs forces you to dive deep in the rabbit hole)