thinking_budget doesn`t work

I use following method to post a request, however the response show the model is still thinking.
```python
data = {
"messages": [
{
"role": "user",
"content": prompt
}
],
"extra_body":{
"chat_template_kwargs": {
"thinking_budget": 0
}
}
}

model = "http://localhost:9476/v1/chat/completions"

out = requests.post(model, json=data).json()["choices"][0]["message"]["content"]
print(out)
```

Start with the Python requests reproduction against http://localhost:9476/v1/chat/completions and trace how extra_body.chat_template_kwargs is handled, especially thinking_budget=0. Verify the behavior with a minimal request and consider the issue done when the response no longer includes model thinking for that setting.

Written by the indexing model from the issue text.