Require auth for the web UI, keep the JSON API open

Sites/Social Accounts/Posts pages now require login; add a Login
Livewire component, guest layout, and logout action. routes/api.php
is untouched, per AI_API.md's documented no-auth-by-design contract.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

app/Livewire/Auth/Login.php

@@ -0,0 +1,40 @@
+<?php
+
+namespace App\Livewire\Auth;
+
+use Illuminate\Support\Facades\Auth;
+use Livewire\Attributes\Layout;
+use Livewire\Component;
+
+#[Layout('components.layouts.guest')]
+class Login extends Component
+{
+    public string $email = '';
+
+    public string $password = '';
+
+    public bool $remember = false;
+
+    public function login(): void
+    {
+        $credentials = $this->validate([
+            'email' => ['required', 'email'],
+            'password' => ['required'],
+        ]);
+
+        if (! Auth::attempt($credentials, $this->remember)) {
+            $this->addError('email', 'These credentials do not match our records.');
+
+            return;
+        }
+
+        request()->session()->regenerate();
+
+        $this->redirect(route('sites.index'), navigate: true);
+    }
+
+    public function render()
+    {
+        return view('livewire.auth.login');
+    }
+}