### Check for existing issues

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

### What happened?

When configuring the LiteLLM proxy with `model: auto_router/complexity_router` inside a model's `litellm_params`, every request returns a 400 BadRequestError:

`litellm.BadRequestError: Unmapped LLM provider for this endpoint. You passed model=complexity_router, custom_llm_provider=auto_router`

When a fallback is configured, the fallback also fails because the router exposes the pre-alias model name (e.g. claude-sonnet-4-6) in the fallback lookup instead of the resolved group name (internal-ai), so no fallback entry matches: `No fallback model group found for original model_group=claude-sonnet-4-6. Fallbacks=[{'internal-ai': ['internal-haiku']}]. Available Model Group Fallbacks=None`

### Steps to Reproduce

1. Define two backend models in model_list (e.g. internal-haiku, internal-sonnet).

2. Define a router model that uses auto_router/complexity_router: ` - model_name: internal-ai litellm_params: model: auto_router/complexity_router complexity_router_config: tiers: SIMPLE: internal…