Firefox doesn't ask permission just to use localstorage, no modern browser does this. The closest thing you get is when a site wants to persist storage with "navigator.storage.persist()", which should prompt you for permission. But localstorage data usually persists anyway, and only gets deleted if the browser's storage is "under pressure", so I've never personally worked on a site or web app that had to use that API.
Firefox doesn't ask permission just to use localstorage, no modern browser does this. The closest thing you get is when a site wants to persist storage with "navigator.storage.persist()", which should prompt you for permission. But localstorage data usually persists anyway, and only gets deleted if the browser's storage is "under pressure", so I've never personally worked on a site or web app that had to use that API.