feat: initialize game frontend with Vue, routing, and session management

- Add index.html as the entry point for the application.
- Create App.vue to serve as the main application component with RouterView.
- Implement global styles in main.css using Tailwind CSS.
- Set up TypeScript definitions for Vue components in env.d.ts.
- Configure Vue Router with routes for home, public, login, and not found views.
- Extend RouteMeta interface to include authentication-related metadata.
- Create a Pinia store for session management with status tracking.
- Implement TRPC client for API communication with session token handling.
- Develop views for Login, Main, Not Found, and Public with basic structure.
- Configure TypeScript for Node with tsconfig.node.json.
- Set up Vite configuration for the project with Vue and Tailwind CSS plugins.

app/game-frontend/src/env.d.ts

@@ -0,0 +1,7 @@
+/// <reference types="vite/client" />
+
+declare module '*.vue' {
+    import type { DefineComponent } from 'vue';
+    const component: DefineComponent<Record<string, never>, Record<string, never>, Record<string, never>>;
+    export default component;
+}