refactor: scope providers by route and use XState selectors

src/app/private-room/layout.tsx

@@ -0,0 +1,11 @@
+import type { ReactNode } from "react";
+
+import { PrivateRoomRouteProvider } from "@/providers/private-room-route-provider";
+
+export default function PrivateRoomLayout({
+  children,
+}: {
+  children: ReactNode;
+}) {
+  return <PrivateRoomRouteProvider>{children}</PrivateRoomRouteProvider>;
+}