Cookies expire in the same way.
Indexed DB, LocalStorage, Media keys, SessionStorage, Service Worker registrations
Since cookies are not mentioned, I'm assuming it's NOT affected by the 7 day cap but will instead continue to work as normal (except for the fact that 3rd party cookies will stop working, which is a Good Thing)
So in order to have a long-lived cookie, you essentially need to treat them as read-only client side, and push any and all update/write logic to the server such that it'll return a set-cookie header with any changes you require.