[EPIC] Refactor stores and migrate to Pinia

Pinia is the recommended central state management solution for Vue3. Apart from that the current store implementations have a few problems, namely:

• some separation-of-concerns-violations, i.e. alert calls that interact with the user instead of setting error states
• inability to react to error states (exceptions are swallowed and turned into alerts)
• code duplication (i.e. setting authentication headers)

Basis for follow-up tasks

Once transitioned we might also

• get rid of the axios dependency which most certainly can be replaced with the browser-native fetch: Refactor: Remove Axios in favour of native fetch() (#279 - closed)
• be able to reduce the overall code size through generic implementations for CRUD operations: TODO: check where we can do generic implementations. Create tickets.
• improve DX by using TypeScript: Improve DX: Use TypeScript or JSDoc (#278 - closed)

Subtasks

• migrate auth store
• migrate files store
• migrate playlists store
• migrate notes store
• migrate schedules store
• migration timeslots store
• migrate shows store
• migrate meta stores (including types, funding-categories, categories, topics, music-focus, languages, and hosts)
• Refactor playlist store to load data on-demand ... (#135 - closed)
• TODO: identify other open sub-tasks, if any.