Migrate Azure OpenAI provider from legacy Chat Completions API to the OpenAI Responses API.
- Switch API endpoint from `/openai/deployments/{deployment}/chat/completions` to `/openai/v1/responses`
- Change auth header from `Api-Key` to `Authorization: Bearer`
- Use `responses.ResponseNewParams` SDK types for request construction
- Extract shared Responses API utilities into `openai_responses_common` package
- Deduplicate 178 lines from codex_provider.go by reusing shared package
- Add 593 lines of comprehensive test coverage for the shared package
Closes#2111
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
Kunal Karmakar