BACKEND: Game Room Engine & WebSocket API

[tosoham]

Implement the real-time core:

• RoomManager class to track rooms, agent states, and player bets

• WebSocket endpoints: /ws/{roomId} for agents & players to exchange messages

• Pydantic models for message schemas

• Graceful room teardown and reconnection handling

Deliverable: Fully functional real-time room engine.

See:

FastAPI WebSockets: https://fastapi.tiangolo.com/advanced/websockets/