Implement Rust shell: tray, global hotkey, overlay window

Frameless transparent always-on-top window, tray icon with toggle/quit,
persisted global hotkey (default Ctrl+Shift+K) with safe re-registration,
single-instance --toggle IPC as Wayland hotkey fallback, close-to-tray.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

package.json

@@ -10,18 +10,21 @@
     "tauri": "tauri"
   },
   "dependencies": {
-    "react": "^19.1.0",
-    "react-dom": "^19.1.0",
     "@tauri-apps/api": "^2",
-    "@tauri-apps/plugin-opener": "^2"
+    "@tauri-apps/plugin-autostart": "^2.5.1",
+    "@tauri-apps/plugin-clipboard-manager": "^2.3.2",
+    "@tauri-apps/plugin-opener": "^2",
+    "@tauri-apps/plugin-store": "^2.4.3",
+    "react": "^19.1.0",
+    "react-dom": "^19.1.0"
   },
   "devDependencies": {
+    "@tauri-apps/cli": "^2",
     "@types/react": "^19.1.8",
     "@types/react-dom": "^19.1.6",
     "@vitejs/plugin-react": "^4.6.0",
     "typescript": "~5.8.3",
-    "vite": "^7.0.4",
-    "@tauri-apps/cli": "^2"
+    "vite": "^7.0.4"
   },
   "allowScripts": {
     "esbuild@0.28.1": true