Make sure reasoning outputs is working as expected in aibrix

### 🚀 Feature Description and Motivation

We need to make sure chat level vs model startup level configuration are compatible.

```
{"enable_thinking": false}
```

1. whether aibrix configuration (gateway) has any limitation?
2. make sure both sglang & vllm are working.
3. update aibrix docs on the version/models etc

- https://docs.vllm.ai/en/latest/features/reasoning_outputs/#disabling-thinking-mode-by-default
- https://qwen.readthedocs.io/en/latest/deployment/sglang.html
- https://developer.volcengine.com/articles/7502283241375760403

### Use Case

enable reasoning mode for end users

### Proposed Solution

_No response_

Start with AIBrix gateway configuration and the vLLM reasoning-outputs and Qwen SGLang deployment references linked in the issue. Check chat-level and model-startup-level enable_thinking behavior for both SGLang and vLLM, then update AIBrix documentation with supported versions, models, and verified configuration.

Written by the indexing model from the issue text.