feat: Support OpenAI Responses API (/v1/responses)

[shohei81]

Summary

This PR adds basic support for the OpenAI /v1/responses API, including
optional streaming support, to improve compatibility with newer OpenAI-based
tooling.

The implementation is intentionally minimal and scoped to:

• Mapping /v1/responses requests into the existing Claude execution flow
• Handling streaming responses in an SSE-compatible manner

This work addresses the feature request discussed in #21.

What’s included

• /v1/responses endpoint support
• Streaming responses (SSE-style)
• No breaking changes to existing endpoints

Testing

• Automated tests: Existing pytest suite passes successfully

No new tests were added in this PR; the change is covered by existing tests.

Notes

If this direction aligns with the project’s design goals, I’m happy to:

• Adjust the API surface or naming
• Reduce or expand the supported response fields
• Split this work into smaller PRs if preferred

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Fixes #21