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/RootNavigator.tsx

@@ -0,0 +1,23 @@
+import React from "react";
+import { ActivityIndicator, View } from "react-native";
+import { useAuth } from "../context/AuthContext";
+import { AuthNavigator } from "./AuthNavigator";
+import { MainNavigator } from "./MainNavigator";
+
+export function RootNavigator() {
+  const { isLoading, isAuthenticated } = useAuth();
+
+  if (isLoading) {
+    return (
+      <View style={{ flex: 1, justifyContent: "center", alignItems: "center" }}>
+        <ActivityIndicator size="large" color="#4a6cf7" />
+      </View>
+    );
+  }
+
+  if (!isAuthenticated) {
+    return <AuthNavigator />;
+  }
+
+  return <MainNavigator />;
+}