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>

resources/views/components/layouts/app.blade.php

@@ -8,10 +8,17 @@
     @livewireStyles
 </head>
 <body class="bg-gray-50 text-gray-900">
-    <nav class="bg-white border-b border-gray-200 px-6 py-4 flex gap-6">
+    <nav class="bg-white border-b border-gray-200 px-6 py-4 flex gap-6 items-center">
         <a href="{{ route('sites.index') }}" class="font-medium hover:text-blue-600">Sites</a>
         <a href="{{ route('social-accounts.index') }}" class="font-medium hover:text-blue-600">Social Accounts</a>
         <a href="{{ route('posts.index') }}" class="font-medium hover:text-blue-600">Posts</a>
+
+        @auth
+            <form method="POST" action="{{ route('logout') }}" class="ml-auto">
+                @csrf
+                <button type="submit" class="text-sm text-gray-500 hover:text-gray-900">Log out</button>
+            </form>
+        @endauth
     </nav>
 
     <main class="p-6">