### Check for existing issues

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

### What happened?

Guardrails can trigger during handling of error response from provider which leads to "exception raised during exception handling" not being properly handled

### Steps to Reproduce

1. Create guardrais which would trigger on content of error message from provider 2. Make such request which would lead to error response from provider 3. Observe broken exception handling in logs

### Relevant log output

```shell 14:37:51 - LiteLLM Proxy:ERROR: proxy_server.py:7096 - litellm.proxy.proxy_server.async_data_generator(): Exception occured - litellm.APIError: APIError: Openrou terException - Message: Provider returned error, Metadata: {'error_type': 'permission_denied'}, User ID: Traceback (most recent call last): File "/app/.venv/lib/python3.13/site-packages/litellm/litellm_core_utils/streaming_handler.py", line 2087, in __anext__ async for chunk in self.completion_stream: # type: ignore[union-attr] ...<84 lines>... return processed_chunk File "/app/.venv/lib/python3.13/site-packages/litellm/llms/base_llm/base_model_iterator.py…