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/App.tsx

@@ -0,0 +1,16 @@
+import React from "react";
+import { NavigationContainer } from "@react-navigation/native";
+import { StatusBar } from "expo-status-bar";
+import { AuthProvider } from "./src/context/AuthContext";
+import { RootNavigator } from "./src/navigation/RootNavigator";
+
+export default function App() {
+  return (
+    <AuthProvider>
+      <NavigationContainer>
+        <StatusBar style="auto" />
+        <RootNavigator />
+      </NavigationContainer>
+    </AuthProvider>
+  );
+}