Streaming LLM Response — Server-Sent Events

## Task
Stream LLM responses token-by-token from server to client using Server-Sent Events.

## Requirements
- Server: Node.js/Next.js API route or Python FastAPI
- Client: React with streaming state management
- LLM: Any provider with streaming support (OpenAI, Anthropic, etc.)

## Server Implementation
```
POST /api/chat
Request: { messages: Message[], model: string }
Response: text/event-stream

Event format:
data: {"token": "Hello"}
data: {"token": " world"}
data: {"done": true, "usage": {"input": 50, "output": 12}}
data: [DONE]
```

## Client Implementation
```
- Use fetch() with ReadableStream, NOT EventSource (POST not supported)
- Parse SSE lines from the stream
- Update UI token by token with requestAnimationFrame batching
- Show typing indicator before first token
- Support abort via AbortController
```

## Implementation Notes
1. Handle backpressure — don't buffer unlimited tokens
2. Add timeout for first token (10s) and between tokens (30s)
3. Client-side: batch DOM updates every 50ms for performance
4. Include error events for graceful failure display
5. Support markdown rendering as tokens arrive (tricky — use incremental parser)
6. Clean up on component unmount (abort controller)