feat: implement lobby functionality with user and server information retrieval

app/gateway-frontend/src/utils/gameTrpc.ts

@@ -0,0 +1,14 @@
+import { createTRPCProxyClient, httpBatchLink } from '@trpc/client';
+import type { appRouter } from '../../../game-api/src/router';
+
+export type GameRouter = typeof appRouter;
+
+export const createGameTrpc = (port: number) => {
+  return createTRPCProxyClient<GameRouter>({
+    links: [
+      httpBatchLink({
+        url: `http://localhost:${port}/api/trpc`, // 실제 환경에서는 도메인/경로 조정 필요
+      }),
+    ],
+  });
+};