It's a bit confusing because there are two similar terms being used to describe this. First is "local storage" which refers to any of the storage, as long as it's on the local device. Second (which you used) is "localStorage", which refers to specifically the window.localStorage API (which you are right about, has been described as a volatile short-term memory for apps).
IndexedDB is also subject to the 7 day limit. Leaving no persistent storage for web apps at all.