[Bug / Tech Debt] Refactor OpenAI responses API protocol: Replace Manual Implementation with SDK-Based Approach

### Description

The current OpenAI Responses API protocol is **largely hand-written based on public documentation**. While this offers initial flexibility, it introduces several critical risks:

- **Inconsistencies with actual API behavior** (e.g., field names, status codes, error formats)
- **Missing edge cases** (rate limits, retry logic, pagination, streaming headers)
- **Hard to maintain** when upstream APIs evolve
- **No type safety or compile-time validation**
- **Duplication of effort** when official SDKs already exist

This has already led to subtle bugs in production—such as malformed JSON payloads, incorrect error handling, or unexpected deserialization failures—especially when integrating with new models or third-party services