rename websocket directory to websocket-chat

Web/WebSocket/websocket-chat/README.md

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+# WebSocket Chat Monorepo
+
+A real-time WebSocket chat application built with TypeScript, Express, and Vite.
+
+## Project Structure
+
+```
+├── apps/
+│   ├── server/          # Express WebSocket server
+│   └── frontend/        # React/Vite frontend
+├── packages/
+│   └── shared-types/    # Shared TypeScript types
+└── package.json         # Root workspace configuration
+```
+
+## Quick Start
+
+```bash
+# Install all dependencies
+npm install
+
+# Start both server and frontend in development mode
+npm start
+
+# Or run individually:
+npm run dev:server    # Start server only
+npm run dev:frontend  # Start frontend only
+```
+
+## Available Scripts
+
+- `npm start` - Build shared types and start both server and frontend
+- `npm run dev:all` - Start both server and frontend concurrently
+- `npm run dev:server` - Start server only
+- `npm run dev:frontend` - Start frontend only
+- `npm run build` - Build all packages
+- `npm run typecheck` - Type check all packages
+- `npm run lint` - Lint all packages
+- `npm run clean` - Clean all build outputs
+
+## Development
+
+The monorepo uses npm workspaces for dependency management and TypeScript project references for type checking across packages.
+
+### Server
+- Runs on `http://localhost:3000`
+- WebSocket endpoint: `ws://localhost:3000/ws`
+- Health check: `http://localhost:3000/ping`
+
+### Frontend
+- Runs on `http://localhost:5173` (Vite default)
+- Connects to WebSocket server for real-time messaging
+
+## Features
+
+- Real-time WebSocket communication
+- Ping/pong latency measurement
+- Shared TypeScript types across packages
+- Hot reload for development
+- Monorepo workspace management