feat: persist project selection

.living_spec/specs/functional/PERSISTENCE.md

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+# Functional Spec: Persistence
+
+## 1. Scope
+The application needs to persist user preferences and session state across restarts.
+The primary use case is remembering the **Last Opened Project**.
+
+## 2. Storage Mechanism
+*   **Library:** `tauri-plugin-store`
+*   **File:** `store.json` (located in the App Data directory).
+*   **Keys:**
+    *   `last_project_path`: String (Absolute path).
+    *   (Future) `theme`: String.
+    *   (Future) `recent_projects`: Array<String>.
+
+## 3. Startup Logic
+1.  **Backend Init:**
+    *   Load `store.json`.
+    *   Read `last_project_path`.
+    *   Verify path exists and is a directory.
+    *   If valid:
+        *   Update `SessionState`.
+        *   Return "Project Loaded" status to Frontend on init.
+    *   If invalid/missing:
+        *   Clear key.
+        *   Remain in `Idle` state.
+
+## 4. Frontend Logic
+*   **On Mount:**
+    *   Call `get_current_project()` command.
+    *   If returns path -> Show Workspace.
+    *   If returns null -> Show Selection Screen.
+*   **On "Open Project":**
+    *   After successful open, save path to store.
+*   **On "Close Project":**
+    *   Clear `SessionState`.
+    *   Remove `last_project_path` from store.
+    *   Show Selection Screen.