Initial commit: Expo app with Better Auth integration

- Complete Expo React Native app setup with TypeScript
- Better Auth authentication system integration
- Secure storage implementation for session tokens
- Authentication flow with login/logout functionality
- API client configuration for backend communication
- Responsive UI components with themed styling
- Expo Router navigation setup
- Development configuration and scripts

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

app/_layout.tsx

@@ -0,0 +1,25 @@
+import { DarkTheme, DefaultTheme, ThemeProvider } from '@react-navigation/native';
+import { Stack } from 'expo-router';
+import { StatusBar } from 'expo-status-bar';
+import 'react-native-reanimated';
+
+import { useColorScheme } from '@/hooks/use-color-scheme';
+
+export const unstable_settings = {
+  anchor: '(tabs)',
+};
+
+export default function RootLayout() {
+  const colorScheme = useColorScheme();
+
+  return (
+    <ThemeProvider value={colorScheme === 'dark' ? DarkTheme : DefaultTheme}>
+      <Stack>
+        <Stack.Screen name="(auth)" options={{ headerShown: false }} />
+        <Stack.Screen name="(tabs)" options={{ headerShown: false }} />
+        <Stack.Screen name="modal" options={{ presentation: 'modal', title: 'Modal' }} />
+      </Stack>
+      <StatusBar style="auto" />
+    </ThemeProvider>
+  );
+}