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/AppNavigator.tsx

@@ -0,0 +1,45 @@
+import { type ReactNode } from "react";
+import { NavigationContainer } from "@react-navigation/native";
+import { createNativeStackNavigator } from "@react-navigation/native-stack";
+import { useAuth } from "../context/AuthContext";
+import LoginScreen from "../screens/LoginScreen";
+import RegisterScreen from "../screens/RegisterScreen";
+import MainTabs from "./MainTabs";
+
+export type AuthStackParamList = {
+  Login: undefined;
+  Register: undefined;
+};
+
+export type RootStackParamList = {
+  Auth: undefined;
+  Main: undefined;
+};
+
+const RootStack = createNativeStackNavigator<RootStackParamList>();
+const AuthStack = createNativeStackNavigator<AuthStackParamList>();
+
+function AuthNavigator(): ReactNode {
+  return (
+    <AuthStack.Navigator screenOptions={{ headerShown: false }}>
+      <AuthStack.Screen name="Login" component={LoginScreen} />
+      <AuthStack.Screen name="Register" component={RegisterScreen} />
+    </AuthStack.Navigator>
+  );
+}
+
+export default function AppNavigator(): ReactNode {
+  const { state } = useAuth();
+
+  return (
+    <NavigationContainer>
+      <RootStack.Navigator screenOptions={{ headerShown: false }}>
+        {state.isAuthenticated ? (
+          <RootStack.Screen name="Main" component={MainTabs} />
+        ) : (
+          <RootStack.Screen name="Auth" component={AuthNavigator} />
+        )}
+      </RootStack.Navigator>
+    </NavigationContainer>
+  );
+}