### Check for existing issues

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

### What happened?

### Describe the bug

When calling the Anthropic passthrough endpoint (`/anthropic/v1/messages`), the response body contains Anthropic's native `msg_...` ID in the `id` field. However, the `request_id` stored in the LiteLLM spend logs is a UUID (`litellm_call_id`). This makes it impossible for clients to correlate a response with its spend log entry using the response body alone.

### Steps to Reproduce

### To Reproduce

1. Send a request to the Anthropic passthrough endpoint:

```bash curl -X POST "http://localhost:4000/anthropic/v1/messages" \ -H "Authorization: Bearer sk-1234" \ -H "Content-Type: application/json" \ -H "Anthropic-Version: 2023-06-01" \ -d '{ "model": "claude-sonnet-4-5-20250929", "max_tokens": 10, "messages": [{"role": "user", "content": "Hello"}] }'

2. Observe the response body contains "id": "msg_01AbCdEfGhIjKlMnOpQrStUv" (Anthropic's original ID). 3. The response header contains x-litellm-call-id: ffcb49e7-bd6e-4e56-9c08-a7243802b26a (LiteLLM-generated UUID). 4. Q…