feat: implement lobby functionality with user and server information retrieval

app/gateway-frontend/src/router/index.ts

@@ -1,5 +1,6 @@
 import { createRouter, createWebHistory } from 'vue-router';
 import HomeView from '../views/HomeView.vue';
+import LobbyView from '../views/LobbyView.vue';
 
 const router = createRouter({
   history: createWebHistory(import.meta.env.BASE_URL),
@@ -9,7 +10,11 @@ const router = createRouter({
       name: 'home',
       component: HomeView,
     },
-    // 추후 추가될 페이지들
+    {
+      path: '/lobby',
+      name: 'lobby',
+      component: LobbyView,
+    },
   ],
 });