P5: Implement streaming chat completions gateway

[wauputr4]

Goal

Add streaming support for /v1/chat/completions while preserving request context, usage capture, and cleanup behavior.

Acceptance Criteria

• Streaming request path proxies provider chunks to the client.
• Final usage metadata is captured when upstream provides it.
• Gateway releases any runtime resources after stream completion or error.
• Streaming works with OpenAI-compatible clients.

[wauputr4]

PR #34 review split the remaining streaming hardening into two focused follow-up issues:

• P5: Stream chat completion chunks end-to-end without buffering #35: P1 true end-to-end streaming without buffering in provider/API layers.
• P5: Support multi-line SSE data fields in provider stream parser #36: P2 support multi-line SSE data fields in the provider stream parser.

These should be treated as the concrete implementation follow-ups for this broader P5 streaming milestone.