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/src/navigation/AuthNavigator.tsx

@@ -0,0 +1,24 @@
+import React from "react";
+import { createNativeStackNavigator } from "@react-navigation/native-stack";
+import LoginScreen from "../screens/LoginScreen";
+import RegisterScreen from "../screens/RegisterScreen";
+
+export type AuthStackParamList = {
+  Login: undefined;
+  Register: undefined;
+};
+
+const Stack = createNativeStackNavigator<AuthStackParamList>();
+
+export function AuthNavigator() {
+  return (
+    <Stack.Navigator
+      screenOptions={{
+        headerShown: false,
+      }}
+    >
+      <Stack.Screen name="Login" component={LoginScreen} />
+      <Stack.Screen name="Register" component={RegisterScreen} />
+    </Stack.Navigator>
+  );
+}