### Summary / feature request

When running the proxy as a gateway with **cross-provider fallbacks** (e.g. `claude-*` → `gemini-*`), consumers that call the **Anthropic `/v1/messages`** endpoint (via `ANTHROPIC_BASE_URL` + the Anthropic SDK) have **no reliable way to tell which model actually served a request** after a fallback. `/v1/chat/completions` already exposes this; `/v1/messages` doesn't. This is a small parity gap that matters a lot for cost attribution, quality tracking, and detecting silent substitutions.

### Current behavior

**`/v1/chat/completions` (good):** - response headers `x-litellm-model-group` and `x-litellm-model-api-base` reflect the **served** model - `body.model` = served model

**`/v1/messages` (gap):** - the only model-ish header is `x-litellm-model-id` — an **opaque deployment hash** - `body.model` **echoes the requested model**, not the served one

So on a fallback (`claude-sonnet-4-6` served by `gemini-3.5-flash`), a `/v1/messages` client sees `"model": "claude-sonnet-4-6"` and cannot detect the substitution.

### Why a user-side callback can't work around it (v1.92.0)

We tried a `CustomLogger.async_post_call_success_hook` to stamp `_hidden_params["a…