Implement the OpenAI `/v1/responses`

[matifali]

Needed for RooCode
Nice to have for now, unless a customer or a popular coding agent requires this explicitly.

[ibetitsmike]

Once done it would be worthwile to make sure this is supported (it's a major use case for this feature):
https://platform.openai.com/docs/models/gpt-5-codex