client: project config and bootstrap

Add Vite + React + TypeScript setup, package.json (react-router-dom,
socket.io-client), global CSS, app entry point and environment
config.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

client/vite.config.ts

@@ -0,0 +1,10 @@
+import { defineConfig } from 'vite';
+import react from '@vitejs/plugin-react';
+
+export default defineConfig({
+  plugins: [react()],
+  server: {
+    port: 5173,
+    host: true,
+  },
+});