Migrate the elements Vuex module to a Pinia store

Migrate the Vuex store module in src/store/elements.js to Pinia with TypeScript, after the related API helpers have been typed, and update all components and tests.

Requires #1137 (closed), #1358 (closed), #1357 (closed), #1139 (closed), and either #1150 (closed) or #1393 (closed).