[Doc]: Update the reasoning output streaming example with OpenAI client

[gaocegege]

📚 The doc issue

We are using requests in the reasoning output streaming example because at that time DeltaMessage does not support custom fields. https://github.com/vllm-project/vllm/blob/main/examples/online_serving/openai_chat_completion_with_reasoning_streaming.py

Here is a contributor in SGLang community verified that OpenAI python client should work now. sgl-project/sglang#3859 (comment)

Suggest a potential alternative/fix

No response

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[cjackal]

I think both the sentence in the vllm example and what @xihuai18 said in the comment are correct:

• openai-python does not officially support (in the sense that ChoiceDelta does not define) reasoning_content attribute for streaming output but define it when the model server response contains it (like when --enable-reasoning-content option is set)
• due to this nature of openai python client, if one branches by whether reasoning_content attribute exists in the ChoiceDelta(e.g. by hasattr(chunk.choices[0].delta, "reasoning_content") check), we are safe to use openai-python for streaming output
• the demo script in sglang has edge case though; if the model sends empty string (like a partial unicode bytes for emoji) in the content field, the nontriviality check(if chunk.choices[0].delta.content:) fails but reasoning_content attribute does not exists, so it raises attribute error.

[gaocegege]

@cjackal

SGTM. We could fall back to the requests-based method if ChoiceDelta is missing in the Python package

[gaocegege]

#14077 addressed it.