Refactor gateway request log persistence to avoid blocking response path

[wauputr4]

Context

Review comment on PR #48 flagged that request logging () is awaited inline in many branches of , which adds synchronous database latency to API responses.

Proposed changes

• Move request-log writes to an async background path (e.g., spawn task or bounded worker queue).
• Keep failure handling resilient: never block/impact user-facing success path if logging fails.
• Preserve existing request metadata (request id, status, provider, route, latency, error_code).
• Add retry or bounded queue behavior to avoid unbounded task growth.

Acceptance Criteria

• Hot path no longer waits for DB INSERT before returning response for chat completions.
• Existing request log rows remain written with same schema and meaningful status/error_code.
• Logging failures are recorded to tracing logs without changing API contract.
• Regression test proves request handler latency path is unaffected by log DB failure.

Notes

Related comments are in PR #48: high-priority suggestion around blocking DB writes in handler flow.