feat: add expo mobile application source code

mobile/app/index.tsx

@@ -0,0 +1,15 @@
+import React from 'react';
+import { Redirect } from 'expo-router';
+import { useAuth } from '../context/AuthContext';
+
+export default function Index() {
+  const { user, isLoading } = useAuth();
+
+  // Wait for auth to settle
+  if (isLoading) return null;
+
+  // Smart redirect: If we have a user with an ID, go to dashboard, otherwise login
+  const isAuthenticated = !!(user && user.id);
+  
+  return <Redirect href={isAuthenticated ? '/(tabs)' : '/(auth)/login'} />;
+}