### Check for existing issues

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

### What happened?

Responses API tool-call state is not closed correctly for Codex CLI through LiteLLM proxy. Repeated Search/Read tool calls occur while direct provider works.

### Steps to Reproduce

1. 2. Codex CLI repeatedly calls the same Search and Read tools when routed through LiteLLM Responses API.

Direct provider works correctly with the same Codex config. When using LiteLLM as proxy, asking Codex to inspect the current repository causes repeated tool calls:

Search ./.git/* in . Read RTK.md Search ./.git/* in . Read RTK.md ...

This looks like the Responses API tool-call state is not closed correctly, or tool results are not associated with the correct call_id / output item when using stream=true and previous_response_id. 3.

### Relevant log output

```shell

```

### What part of LiteLLM is this about?

_No response_

### What LiteLLM version are you on ?

v1.88.0

### Twitter / LinkedIn details

_No response_