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/babel.config.js

@@ -0,0 +1,7 @@
+module.exports = function (api) {
+  api.cache(true);
+  return {
+    presets: ["babel-preset-expo"],
+    plugins: ["react-native-reanimated/plugin"],
+  };
+};