### Check for existing issues

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

### What happened?

When routing through a model group, the `model` field emitted in the standard logging payload — and therefore what shows up in spend logs and every downstream logging callback that reads it — is **not stable across the outcome of the request**. The same logical call is labeled with two different model strings depending on whether it succeeded or failed:

- **Successful request** → `model` = the backend deployment model, i.e. the value from `litellm_params.model` (the "LiteLLM Model" in the UI), e.g. `anthropic/claude-sonnet-4-6`. - **Failed request** → `model` = the requested model-group alias, i.e. the `model_name` the caller sent (the public "Model Name" in the UI), e.g. `ssg/anthropic-claude-sonnet-4-6`.

We first noticed this on Anthropic `529 overloaded_error` responses (an upstream capacity error, not a client/config problem), but the trigger is not specific to 529 — it applies to the failure logging path generally, whereas the success path consistently logs the resolved deployment model.

Concretely, in our setup a single model group def…