## Bug Summary

`litellm.responses()` / `litellm.aresponses()` silently drops the `timeout` parameter when routing through the **completion transformation path** (used by Anthropic, Vertex AI Claude, Bedrock, and any provider without a native Responses API config). The timeout works correctly on the **native Responses API path** (OpenAI, Azure).

This means `Router(timeout=40)` is a no-op for Anthropic models using the Responses API. The actual timeout falls back to the Anthropic SDK default (~600s).

## Production Impact

- **Incident**: A single `aresponses()` call to `claude-sonnet-4-6` hung for **602.7 seconds** despite `Router(timeout=40)`. - **Root cause**: The 602.7s matches the Anthropic SDK default timeout (~600s), confirming the Router's `timeout=40` was never enforced.

## Bug Location

**File**: `litellm/responses/main.py` — `responses()` function

### The problem (line ~1108 on current `main`)

```python # COMPLETION TRANSFORMATION PATH (Anthropic, Bedrock, etc.) # timeout is a NAMED PARAMETER of responses(), so it is NOT in **kwargs if responses_api_provider_config is None or use_chat_completions_api is True: return litellm_completion_transformation_handler.respon…