feat: implement gate authentication with login and logout functionality

resources/views/layouts/app.blade.php

@@ -134,6 +134,15 @@
            class="nav-item {{ request()->routeIs('settings.*') ? 'active' : '' }}">
             <span class="text-lg shrink-0">🔔</span> Notifications
         </a>
+
+        {{-- Logout --}}
+        <form method="POST" action="{{ route('gate.logout') }}" class="mt-auto pt-4">
+            @csrf
+            <button type="submit"
+                    class="nav-item w-full text-left text-gray-400 hover:text-red-400 hover:bg-red-50 transition-colors">
+                <span class="text-lg shrink-0">🚪</span> Lock App
+            </button>
+        </form>
     </nav>
 </aside>