Feature: Flush response headers immediately for streaming requests #40

Problem

When a Chat Completions provider has high time-to-first-token (e.g., GLM-5.2 with large context can take 20-90s before first token), codex-relay does not flush the HTTP response headers until the first SSE event arrives.

This causes client-side idle timeouts ("stream disconnected before completion: idle timeout waiting for SSE") because the client sees no HTTP response at all during the TTFT period.

Current workaround

Proxy scripts must:

1. Send HTTP 200 + headers to the client immediately (before forwarding to codex-relay)
2. Inject SSE keepalive comments (": keepalive\n\n") every 5 seconds during TTFT
3. Stop keepalives once real output begins

This is ~40 lines of keepalive management that would be unnecessary if codex-relay flushed headers early.

Proposed solution

codex-relay could:

1. Send HTTP 200 + Content-Type: text/event-stream headers immediately when accepting a streaming request
2. Optionally send SSE keepalive comments while waiting for the upstream's first token

Environment

• codex-relay 0.5.1
• GLM-5.2 via Chat Completions (TTFT 5-90s for large context)