refactor: rename web/ to api/ to better reflect its purpose

The web/ folder contains the REST API, WebSocket server, and OAuth
routes — not a web frontend. Renaming to api/ clarifies this distinction
since the actual web frontend lives in panel/.

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

api/README.md

@@ -0,0 +1,30 @@
+# Aurora Web API
+
+The web API provides a REST interface and WebSocket support for accessing Aurora bot data and configuration.
+
+## API Endpoints
+
+- `GET /api/stats` - Real-time bot statistics
+- `GET /api/settings` - Bot configuration
+- `GET /api/users` - User data
+- `GET /api/items` - Item catalog
+- `GET /api/quests` - Quest information
+- `GET /api/transactions` - Economy data
+- `GET /api/health` - Health check
+
+## WebSocket
+
+Connect to `/ws` for real-time updates:
+- Stats broadcasts every 5 seconds
+- Event notifications via system bus
+- PING/PONG heartbeat support
+
+## Development
+
+The API runs automatically when you start the bot:
+
+```bash
+bun run dev
+```
+
+The API will be available at `http://localhost:3000`