feat: persist project selection

.living_spec/specs/tech/STACK.md

@@ -81,9 +81,11 @@ To support both Remote and Local models, the system implements a `ModelProvider`
     *   `uuid`: For unique message IDs.
     *   `chrono`: For timestamps.
     *   `tauri-plugin-dialog`: Native system dialogs.
+    *   `tauri-plugin-store`: Persistent key-value storage.
 *   **JavaScript:**
     *   `@tauri-apps/api`: Tauri Bridge.
     *   `@tauri-apps/plugin-dialog`: Dialog API.
+    *   `@tauri-apps/plugin-store`: Store API.
     *   `react-markdown`: For rendering chat responses.
 
 ## Safety & Sandbox