### Check for existing issues

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

### What happened?

When using **OpenAI Codex** (or other clients that use the Responses API) with an **Azure provider** model through LiteLLM proxy, all streaming requests fail with:

``` Unknown parameter: 'stream_options.include_usage'. ```

Codex Desktop sends streaming Responses API requests to `/v1/responses` with `stream: true`. The client does **not** include `stream_options` in the request body (verified by capturing raw Codex requests with a debug HTTP server). However, LiteLLM internally injects `stream_options: {"include_usage": true}` before forwarding the request to Azure. Azure's Responses API does not accept this parameter (it is only valid for the Chat Completions API), so the request is rejected with HTTP 400.

In our testing, this issue occurs across multiple Azure-deployed models (gpt-5.4, gpt-5.5), not limited to a specific model. Chat Completions API (`/v1/chat/completions`) with the same Azure models works fine because Chat Completions supports `stream_options`.

**Expected behavior:** Codex streaming Responses API requests to Azure models s…