Remove social auth and stabilize email/password flow

frontend/app/auth/signup/page.tsx

@@ -1,15 +1,25 @@
 'use client';
 
-import { signUp } from '@/lib/better-auth';
-import { useState } from 'react';
+import { signUp, useSession } from '@/lib/better-auth';
+import { useRouter } from 'next/navigation';
+import { useEffect, useState } from 'react';
 
 export default function SignUp() {
+  const { data: session, isPending: sessionPending } = useSession();
+  const router = useRouter();
+
   const [name, setName] = useState('');
   const [email, setEmail] = useState('');
   const [password, setPassword] = useState('');
   const [loading, setLoading] = useState(false);
   const [error, setError] = useState('');
 
+  useEffect(() => {
+    if (!sessionPending && session?.user) {
+      router.replace('/');
+    }
+  }, [sessionPending, session, router]);
+
   const handleSignUp = async (e: React.FormEvent) => {
     e.preventDefault();
     setLoading(true);
@@ -25,7 +35,8 @@ export default function SignUp() {
       if (result.error) {
         setError(result.error.message || 'Sign up failed');
       } else {
-        window.location.href = '/';
+        router.replace('/');
+        router.refresh();
       }
     } catch (err) {
       setError('Sign up failed');
@@ -94,7 +105,7 @@ export default function SignUp() {
 
           <button
             type="submit"
-            disabled={loading}
+            disabled={loading || sessionPending}
             className="w-full bg-gradient-to-r from-blue-500 to-purple-500 hover:from-blue-600 hover:to-purple-600 text-white font-semibold py-3 rounded-lg transition disabled:opacity-50 disabled:cursor-not-allowed"
           >
             {loading ? 'Creating account...' : 'Sign Up'}