Migrate the search Vuex store moduel to a Pinia store

Requires !1512 (merged), !1517 (merged) and !1518 (merged), closes #1157 (closed), resolves ARKINDEX-FRONTEND-B5A

The store itself is not that complicated, but typing the 3 search components and the search view is complex. This made me find out that Vue Router types the route's query string in a rather complicated way that translates to { [name: string]: string | null | (string | null)[] }, which made me discover a whole bunch of bugs in many pages of the frontend that will be resolved by TypeScripting everything. There are many explicit casts (something as SomeType) because various complicated details of JavaScript objects and iterators end up making TypeScript forget about more specific types like SearchSort, casting it back to a mere string.