chore: initial project scaffold with Fastify server and Vite React app

Set up monorepo structure with server/ (Fastify + TypeScript) and web/ (React + Vite + TypeScript).
Includes package configs, dev proxy setup, and mobile-first CSS foundation.

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

web/vite.config.ts

@@ -0,0 +1,16 @@
+import { defineConfig } from 'vite';
+import react from '@vitejs/plugin-react';
+
+export default defineConfig({
+  plugins: [react()],
+  server: {
+    port: 5173,
+    proxy: {
+      '/api': 'http://localhost:3000',
+      '/socket.io': {
+        target: 'http://localhost:3000',
+        ws: true,
+      },
+    },
+  },
+});