Design a Svelte Store with Derived State and Async Subscriptions

Create a custom Svelte store (compatible with [SVELTE_VERSION]: Svelte 4 or Svelte 5 runes) for managing [STORE_PURPOSE] (e.g., shopping cart, authentication state, theme preferences, notification queue, multi-step form wizard). Store Requirements: - State shape: [STATE_SHAPE_DESCRIPTION] - Must support: [FEATURE_LIST] (e.g., persistence, optimistic updates, undo/redo, real-time sync) - Data source: [DATA_SOURCE] (e.g., REST API, localStorage, WebSocket, IndexedDB) Please implement the following: 1. **Store Definition**: Create a custom store using `writable()` with a custom `set`/`update` contract (or Svelte 5 `$state` rune if specified). Define the TypeScript interface for the store's state. 2. **Custom Methods**: Extend the store with domain-specific methods exposed via the store's return object: - [ACTION_1]: [ACTION_1_DESCRIPTION] - [ACTION_2]: [ACTION_2_DESCRIPTION] - [ACTION_3]: [ACTION_3_DESCRIPTION] Ensure each method properly calls `update()` or `set()` to trigger reactivity. 3. **Derived Stores**: Create `derived()` stores for computed values: - [DERIVED_1]: computed from [DERIVATION_LOGIC_1] - [DERIVED_2]: computed from [DERIVATION_LOGIC_2] Handle async derived values if needed using the `set` callback pattern. 4. **Persistence Layer**: Implement automatic synchronization with [DATA_SOURCE]: - Save state on changes (debounced at [DEBOUNCE_MS]ms) - Load initial state on store creation - Handle serialization/deserialization for complex types (Dates, Maps, Sets) - Graceful fallback when [DATA_SOURCE] is unavailable 5. **Subscription Side Effects**: Add a custom `subscribe` wrapper or `start`/`stop` logic for side effects that activate when the first subscriber connects and clean up when the last one disconnects. 6. **Error State & Loading**: Incorporate loading and error states within the store. Expose `isLoading` and `error` as derived or nested state. 7. **Store Contract**: Ensure the store satisfies Svelte's store contract (`subscribe` method returning an `unsubscribe` function) for use with `$` auto-subscription syntax. 8. **Component Example**: Show a Svelte component using the store with `$` prefix bindings, demonstrating [COMPONENT_SCENARIO] including reactive updates, method calls, and derived value display. Add inline documentation and export the store as a singleton with an optional factory function for testing.