feat(ui): move admin panel and join-game into profile dropdown

- Replace header admin link + profile modal with a dropdown menu
- Dropdown contains: profile, settings, admin (admins only), join-game form, logout
- Remove join-game card from homepage for logged-in users (now in dropdown)
- AuthModal now only handles guest/login/register flows

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

client/src/app/page.tsx

@@ -82,21 +82,8 @@ export default function Home() {
       {/* Laufende Partien – Live-Kacheln */}
       <LiveGames />
 
-      {/* Öffentliche Spiele + Beitreten */}
-      <div className={`grid gap-6 grid-cols-1 ${isLoggedIn ? "lg:grid-cols-3" : ""}`}>
-        <div className={isLoggedIn ? "lg:col-span-2" : ""}>
-          <PublicGames />
-        </div>
-        {isLoggedIn && (
-          <div className="card bg-base-200 shadow h-fit">
-            <div className="card-body">
-              <h2 className="card-title text-lg">🔗 Einladung annehmen</h2>
-              <p className="text-sm opacity-70 mb-2">Link oder Code eingeben</p>
-              <JoinGame />
-            </div>
-          </div>
-        )}
-      </div>
+      {/* Öffentliche Spiele */}
+      <PublicGames />
 
     </div>
   );