feat: initialize gateway frontend with Vue 3, Vite, and Tailwind CSS

- Set up pnpm workspace with necessary dependencies including esbuild and vue-demi.
- Create initial HTML structure for the frontend application.
- Implement main App component with Vue Router integration.
- Add global styles using Tailwind CSS and custom theme variables.
- Define TypeScript environment for Vue components.
- Create a default layout component for consistent page structure.
- Set up Vue Router with a home view route.
- Implement authentication store using Pinia for user management.
- Create utility for tRPC client setup.
- Develop HomeView component with login functionality and server status placeholder.
- Configure TypeScript for Node with composite and strict options.
- Set up Vite configuration for Vue and Tailwind CSS integration.

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

@@ -0,0 +1,16 @@
+import { createRouter, createWebHistory } from 'vue-router';
+import HomeView from '../views/HomeView.vue';
+
+const router = createRouter({
+  history: createWebHistory(import.meta.env.BASE_URL),
+  routes: [
+    {
+      path: '/',
+      name: 'home',
+      component: HomeView,
+    },
+    // 추후 추가될 페이지들
+  ],
+});
+
+export default router;