## Bug Description

The config key `use_chat_completions_url_for_anthropic_messages` is not respected when set in `litellm_settings` in the LiteLLM proxy configuration YAML.

## Root Cause

In `litellm/llms/anthropic/experimental_pass_through/messages/handler.py`:

```python _RESPONSES_API_PROVIDERS = frozenset({"openai"})

def _should_route_to_responses_api(custom_llm_provider: Optional[str]) -> bool: if litellm.use_chat_completions_url_for_anthropic_messages: return False return custom_llm_provider in _RESPONSES_API_PROVIDERS ```

The module-level variable `litellm.use_chat_completions_url_for_anthropic_messages` is **never populated from the proxy config YAML**. Setting `use_chat_completions_url_for_anthropic_messages: true` under `litellm_settings` has no effect because the config parsing code does not map this key to the `litellm` module attribute.

## Reproduction Steps

1. Configure LiteLLM proxy with an `openai/`-prefixed vLLM backend 2. Set `use_chat_completions_url_for_anthropic_messages: true` in `litellm_settings` in the proxy config YAML 3. Send an Anthropic Messages API request through the proxy (e.g., via Claude Code with `ANTHROPIC_BASE_URL` pointing…