feat: Integrate Expo mobile application into monorepo (#16)

- Add mobile/ directory with Expo React Native project
- Create API client with JWT auth and token refresh using AsyncStorage
- Implement AuthContext for login/register/logout flow
- Add screens: Login, Register, Library, Search, Settings
- Set up React Navigation with AuthStack and MainTabs
- Create packages/shared/ with shared types and utilities
- Add shared validation utilities (email, password strength)
- Update root package.json workspaces to include mobile + shared
- Add spec document docs/backend/009-expo-integration.md

mobile/tsconfig.json

@@ -0,0 +1,20 @@
+{
+  "compilerOptions": {
+    "target": "ES2022",
+    "lib": ["ES2023"],
+    "module": "ESNext",
+    "moduleResolution": "bundler",
+    "allowImportingTsExtensions": true,
+    "jsx": "react-jsx",
+    "strict": true,
+    "skipLibCheck": true,
+    "noEmit": true,
+    "forceConsistentCasingInFileNames": true,
+    "baseUrl": ".",
+    "paths": {
+      "@/*": ["src/*"]
+    }
+  },
+  "include": ["**/*.ts", "**/*.tsx"],
+  "exclude": ["node_modules"]
+}