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/stores/session.ts

@@ -0,0 +1,23 @@
+import { defineStore } from 'pinia';
+
+export type SessionStatus = 'unknown' | 'public' | 'authed' | 'general';
+
+interface SessionState {
+    status: SessionStatus;
+}
+
+export const useSessionStore = defineStore('session', {
+    state: (): SessionState => ({
+        status: 'unknown',
+    }),
+    getters: {
+        isReady: (state) => state.status !== 'unknown',
+        isAuthed: (state) => state.status === 'authed' || state.status === 'general',
+        hasGeneral: (state) => state.status === 'general',
+    },
+    actions: {
+        setStatus(status: SessionStatus) {
+            this.status = status;
+        },
+    },
+});