implement frontend skeleton with tab navigation and service layer

- Add tab-based navigation (Chat, Calendar) using Expo-Router
- Create auth screens (login, register) as skeletons
- Add dynamic routes for event detail and note editing
- Implement service layer (ApiClient, AuthService, EventService, ChatService)
- Add Zustand stores (AuthStore, EventsStore) for state management
- Create EventCard and EventConfirmDialog components
- Update CLAUDE.md with new frontend architecture documentation
- Add Zustand and FlashList to technology stack

apps/client/src/app/register.tsx

@@ -0,0 +1,45 @@
+import { View, Text, TextInput, Pressable } from 'react-native';
+import BaseBackground from '../components/BaseBackground';
+
+const RegisterScreen = () => {
+  // TODO: Email input field
+  // TODO: Display name input field
+  // TODO: Password input field
+  // TODO: Password confirmation field
+  // TODO: Register button -> AuthService.register()
+  // TODO: Link to LoginScreen
+  // TODO: Error handling and display
+  // TODO: Navigate to Calendar on success
+  throw new Error('Not implemented');
+
+  return (
+    <BaseBackground>
+      <View className="flex-1 justify-center items-center p-4">
+        <Text className="text-2xl mb-8">Register</Text>
+        <TextInput
+          placeholder="Email"
+          className="w-full border rounded p-2 mb-4"
+        />
+        <TextInput
+          placeholder="Display Name"
+          className="w-full border rounded p-2 mb-4"
+        />
+        <TextInput
+          placeholder="Password"
+          secureTextEntry
+          className="w-full border rounded p-2 mb-4"
+        />
+        <TextInput
+          placeholder="Confirm Password"
+          secureTextEntry
+          className="w-full border rounded p-2 mb-4"
+        />
+        <Pressable className="bg-blue-500 p-3 rounded w-full">
+          <Text className="text-white text-center">Register</Text>
+        </Pressable>
+      </View>
+    </BaseBackground>
+  );
+};
+
+export default RegisterScreen;