## What happened?

Anthropic native `/v1/messages` cost tracking can use the wrong custom price when multiple router deployments share the same public `model_name`.

In this setup, the proxy response header `x-litellm-model-id` shows the actual selected deployment id, but `x-litellm-response-cost-original` / spend can be calculated with another deployment's custom pricing from the same public model group.

This affects Anthropic Messages clients that call LiteLLM with the Anthropic-native API shape instead of `/chat/completions`.

## Expected behavior

Cost tracking should use the actual router-selected deployment `model_info.id` and that deployment's custom pricing for `/v1/messages`, including passthrough/non-streaming paths. The deployment id used for `x-litellm-model-id` should match the deployment id used for custom pricing lookup.

## Actual behavior

When two deployments share one public model group but have different `model_info` custom pricing, a `/v1/messages` request can be routed to provider-b while response cost/spend is calculated using provider-a's pricing.

## Minimal config shape

```yaml model_list: - model_name: claude-public litellm_params: model: an…