### Check for existing issues

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

### The Feature

I would like LiteLLM Router to support protocol-aware deployment selection.

For the same logical model, different deployments may support different request protocols or endpoint styles, for example:

- OpenAI Chat Completions - OpenAI Responses API - Anthropic Messages - provider-specific OpenAI-compatible chat endpoints

Suggested behavior:

1. Each deployment can declare supported protocols or endpoint capabilities. 2. Router detects the incoming request protocol. 3. Router only selects deployments that are compatible with the request protocol. 4. Fallback and retry should preserve protocol compatibility. 5. If no compatible deployment exists, LiteLLM should return a clear error.

Example config direction:

```yaml model_list: - model_name: my-logical-model litellm_params: model: openai/my-provider-model model_info: supported_protocols: - openai_chat_completions

- model_name: my-logical-model litellm_params: model: anthropic/my-provider-model model_info: supported_protocols: - anthrop…