Support for OpenAI Responses API

[mikesir87]

Summary

Add support for the OpenAI Responses API - https://platform.openai.com/docs/api-reference/responses

Reasoning

The Responses API is starting to become the default endpoint used by libraries. For example, the @ai-sdk/openai library's docs state:

Since AI SDK 5, the OpenAI responses API is called by default (unless you specify e.g. 'openai.chat')

While they have fallbacks, higher-level abstractions may not provide the level of configuration needed to swap the endpoint being used.