feat: Initialize QuizMaster Live project

This commit sets up the foundational structure for the QuizMaster Live application. It includes:
- Initializing a new Vite project with React and TypeScript.
- Configuring project dependencies and build tools (Vite, TypeScript).
- Defining core application types for game state, players, questions, etc.
- Setting up basic Tailwind CSS for styling and defining custom animations.
- Integrating with the Google Gemini API for AI-powered question generation.
- Configuring environment variables for API keys and defining the application's metadata.
- Adding a README with setup instructions and local development guide.

index.tsx

@@ -0,0 +1,15 @@
+import React from 'react';
+import ReactDOM from 'react-dom/client';
+import App from './App';
+
+const rootElement = document.getElementById('root');
+if (!rootElement) {
+  throw new Error("Could not find root element to mount to");
+}
+
+const root = ReactDOM.createRoot(rootElement);
+root.render(
+  <React.StrictMode>
+    <App />
+  </React.StrictMode>
+);