Initialize Stage 0: Next.js 16 scaffold with auth and role-based routing

- Next.js 16.2.2 + React 19 + TypeScript + Tailwind v4
- Better Auth with email/password and role system (student/curator/admin)
- Prisma 7 schema: User, Session, Account, Verification + full LMS model
- Role-based dashboards: student /dashboard, curator /curator/dashboard, admin /admin/dashboard
- Auth pages: login, register, verify-email
- Better Auth API route handler
- Middleware for route protection
- Docker Compose with PostgreSQL 16
- Seed script with test users (admin/curator/student)
- CLAUDE.md and ROADMAP.md project documentation

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

src/components/layout/logout-button.tsx

@@ -0,0 +1,23 @@
+"use client";
+
+import { useRouter } from "next/navigation";
+import { signOut } from "@/lib/auth-client";
+
+export function LogoutButton() {
+  const router = useRouter();
+
+  async function handleLogout() {
+    await signOut();
+    router.push("/login");
+    router.refresh();
+  }
+
+  return (
+    <button
+      onClick={handleLogout}
+      className="text-sm text-gray-500 hover:text-gray-700 transition-colors"
+    >
+      Выйти
+    </button>
+  );
+}