### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### The Feature

## Summary Please support direct upstream `/responses` calls for `github_copilot` in `litellm.responses(...)` instead of falling back to the Chat API or a hardcoded endpoint.

## Current behavior With `github_copilot`, `litellm.responses(...)` currently routes GPT-5.6 models through the Chat API (`/chat/completions`) and uses a hardcoded internal endpoint instead of the URL returned during OAuth authentication.

## Requested behavior If the model is a GPT-5.6 variants (or if the endpoint returned during authentication supports `/responses`), please route `litellm.responses(...)` directly to the upstream `/responses` endpoint.

### Motivation, pitch

I'm using `github_copilot` with LiteLLM.

I found that, to call models such as GPT-5.6 on GitHub Copilot, the Responses API is required. However, when I use the `github_copilot` provider through LiteLLM, I found that `litellm.responses(...)` does not route to the actual upstream `/responses` endpoint and instead falls back to Chat API behavior.

Additionally, the endpoint URL is hardcoded and does not…