Earlier quoted context omitted.
It’s trivial to emulate cookies with other Web APIs (storage + service worker, for one). You’re focusing on the label of the toggle and not user intent. If a website can send information about my visit 2 days ago to an upstream server, clearly my expectation of “Disable cookies” is broken.
Then it should be called disable client persistence or something more clear, imo. Cookies is already a ridiculous jargon word esp for the general public.
Seems clear and to the point.