Proposal: Port from chat completions to responses API

[pamelafox]

We've debated porting this repo to use an agent framework (like Microsoft agent-framework), but I think the next right step is to port from chat completions to responses API.

This should hopefully be a much smaller change, and brings about two benefits:

1. Compatibility with more models, like Claude on Azure, which only supports responses: https://github.com/Azure-Samples/claude-with-openai-responses/
2. Easy ability to bring in built-in tools from Azure like Code interpreter.

The main drawback is lack of compatibility with providers that only support chat completions, like Ollama. However, we never added formal support for Ollama to this repo, and we generally need really powerful LLMs for accurate RAG, so there is not as big of a use case for it.

[bf-2026]

It sounds plausible.