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/views/LoginView.vue

@@ -0,0 +1,8 @@
+<script setup lang="ts"></script>
+
+<template>
+    <main class="min-h-screen px-6 py-8">
+        <h1 class="text-2xl font-semibold">Login</h1>
+        <p class="mt-2 text-sm text-amber-200/80">Authentication entry point.</p>
+    </main>
+</template>

app/game-frontend/src/views/MainView.vue

@@ -0,0 +1,10 @@
+<script setup lang="ts"></script>
+
+<template>
+    <main class="min-h-screen px-6 py-8">
+        <h1 class="text-2xl font-semibold">Game Home</h1>
+        <p class="mt-2 text-sm text-amber-200/80">
+            Authenticated main screen placeholder.
+        </p>
+    </main>
+</template>

app/game-frontend/src/views/NotFoundView.vue

@@ -0,0 +1,10 @@
+<script setup lang="ts"></script>
+
+<template>
+    <main class="min-h-screen px-6 py-8">
+        <h1 class="text-2xl font-semibold">Not Found</h1>
+        <p class="mt-2 text-sm text-amber-200/80">
+            The requested page does not exist.
+        </p>
+    </main>
+</template>

app/game-frontend/src/views/PublicView.vue

@@ -0,0 +1,10 @@
+<script setup lang="ts"></script>
+
+<template>
+    <main class="min-h-screen px-6 py-8">
+        <h1 class="text-2xl font-semibold">Public Lobby</h1>
+        <p class="mt-2 text-sm text-amber-200/80">
+            Public cached map and world trend entry point.
+        </p>
+    </main>
+</template>