Add OpenAI Responses support

Given the release of the responses [api](https://platform.openai.com/docs/api-reference/responses/create), we should add support. This might require us to expand the `Provider` enum to `Provider::OpenAIChat` and `Provider::OpenAIResponse` or something similar

Start with the linked OpenAI Responses API documentation and locate the Provider enum mentioned in the issue. Trace how the existing OpenAI provider path is represented, then determine the required support boundaries. Done means the project can use the Responses API through an appropriate provider representation, with behavior verified by the repository's existing checks.

Written by the indexing model from the issue text.