Support the new OpenAI Responses API

[vgrunner4v]

OpenAI has been recommending /responses over /chat/completions for new projects, it would be awesome to stay in sync with OpenAI's updates for compatibility.

Also, it seem to be basically a more clean redesign of /chat/completions api.

• Intro
  https://openai.com/index/new-tools-for-building-agents/

• OpenAI Responses api reference
  https://platform.openai.com/docs/api-reference/responses

• OpenAI Responses vs. Chat Completions
  https://platform.openai.com/docs/guides/responses-vs-chat-completions

Any thoughts on integrating it in llama.cpp server?