### Check for existing issues

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

### What happened?

When making requests to the LiteLLM Proxy via the Anthropic-compatible endpoint (`/v1/messages`), custom proxy-level hooks defined in `CustomLogger` (such as `async_pre_call_hook`) are completely bypassed and not executed.

However, when hitting the standard OpenAI-compatible endpoints (e.g. `/chat/completions` or `/v1/chat/completions`), these exact same hooks are successfully triggered.

Any request routed through the proxy, regardless of whether it originates from the OpenAI `/v1/chat/completions` endpoint or the Anthropic `/v1/messages` endpoint, should reliably trigger the configured `async_pre_call_hook` callbacks.

### Steps to Reproduce

1. Create a custom callback script `custom_hook.py` that inherits from `CustomLogger` and implements `async_pre_call_hook`: ```python import sys from litellm.integrations.custom_logger import CustomLogger

class MyCustomHook(CustomLogger): async def async_pre_call_hook(self, user_api_key_dict, cache, data, call_type, **kwargs): print(">>> async_pre_call_hook EXECUTED!", file=sys.stderr) …