### Check for existing issues

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

### What happened?

**Description** When adding a vector store and specifying the `embedding_model` using a model mapping public model name, the request fails with a `BadRequestError` indicating that the LLM provider is not provided.

**Additional Context**

* The `embedding_model` is using a model mapping public model name (`test-vector-store/bedrock/...`) rather than a direct provider-prefixed model name. * It appears that the provider (`bedrock`) is not correctly inferred from the mapped model name.

**Possible Root Cause** The model mapping resolution may not properly extract or propagate the underlying provider (`bedrock`) when a public model name is used.

**Suggested Fix** Ensure that when a model mapping public name is used:

* The underlying provider is correctly resolved and passed to LiteLLM, or * The mapping layer injects the provider before making the downstream call.

### Steps to Reproduce

1. Create a vector store with the following payload:

```json { "vector_store_id": "my-embeddings:test-index", "custom_llm_provider": "s3_vectors", …