[Feature][Responses API] Streaming ID Alignment

[simon-mo]

🚀 The feature, motivation and pitch

Currently responses API don't output the right IDs for content and ID.

vllm/vllm/entrypoints/openai/serving_responses.py

Lines 815 to 818 in c32e6ad

	current_content_index = 0 # FIXME: this number is never changed
	current_output_index = 0
	current_item_id = "" # FIXME: this number is never changed
	sent_output_item_added = False

Alternatives

No response

Additional context

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[nbishtawi]

Hi! I'm interested in working on this issue but I'm new to the codebase. Would it be okay if I attempted this?

[heheda12345]

Sure. It is a good starting point.

[yeqcharlotte]

Should be addressed with #24788 @qandrew