Fix remaining errors needed to make this directory typecheck with
`noImplicitAny`.

 - Add missing types

 - Use `Object.entries` instead of `for..in` for record iteration in
   several places. Add an `entries` utility to make iteration over
   `Record<Key, Value>` types more convenient where `Key` is more
   specific than just a string.

 - Change localStorage fallback to use a Map rather than object for
   temporary data storage