Add dynamic footer badge marquee with admin management.

Store badges in Postgres, expose public/admin APIs, render an infinite footer slider, and ship /admin for paste-embed CRUD.

Co-authored-by: Cursor <cursoragent@cursor.com>

app/admin/page.tsx

@@ -0,0 +1,26 @@
+import { AdminBadgePanel } from "@/components/AdminBadgePanel";
+
+export const metadata = {
+  title: "Admin · Footer badges · Songs2VID",
+  robots: { index: false, follow: false },
+};
+
+export default function AdminBadgesPage() {
+  return (
+    <main className="min-h-screen bg-surface-dark text-gray-100">
+      <div className="mx-auto max-w-3xl px-6 py-10">
+        <header className="mb-8">
+          <p className="text-xs font-semibold uppercase tracking-wider text-gray-500">
+            Admin
+          </p>
+          <h1 className="mt-1 text-2xl font-bold text-white">Footer badges</h1>
+          <p className="mt-2 text-sm text-gray-400">
+            Manage the infinite badge marquee on the public site footer. Only active badges are
+            shown.
+          </p>
+        </header>
+        <AdminBadgePanel />
+      </div>
+    </main>
+  );
+}