### Check for existing issues

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

### What happened?

I point Claude Code at the LiteLLM proxy and route to a Fireworks model (fw-glm-5.2) deployed on Azure AI Foundry via the `azure_ai` provider. The first turn works. As soon as an assistant turn that contained a `thinking` block is echoed back as history (which Anthropic-format clients like Claude Code always do on multi-turn tool-use), the next request fails with HTTP 400 from the upstream:

```json {"error":{"object":"error","type":"invalid_request_error","code":"invalid_request_error","message":"Extra inputs are not permitted, field: 'messages[2].thinking_blocks', value: [{'type': 'thinking','thinking': 'The user wants me to read a file. Let me read it.','signature': '','cache_control': {}}]"}} ```

This happens on a simple "read a file" turn, i.e. the second message after a thinking-bearing assistant response.

### Root cause

Claude Code talks to the proxy in Anthropic `/v1/messages` format. For the `azure_ai` provider there is no native Anthropic-messages config, so `anthropic_messages_handler` routes through `LiteLLMMessagesToCompletionTr…