[gpt-oss][1][bugfix] fix streaming final output

[qandrew]

Purpose

• currently, response.output in streaming doesn't output a final output because the logic for _messages in StreamingHarmonyContext and HarmonyContext is different. This PR changes StreamingHarmonyContext so it also respects num_init_messages.

per @chaunceyjiang's comments, I've also split up this PR into a couple follow ups:

• [gpt-oss][1a] create_responses stream outputs BaseModel type, api server is SSE still #24759 changes the output of created_responses to AsyncGenerator[BaseModel] from AsyncGenerator[str] and only the API server outputs in SSE format
• [gpt-oss][1b] streaming add item id, content id #24788: add item_id, content_index_id properly

Test Plan

• Spun up server, sent curl requests to confirm the above features work accordingly
• edited unit test

Test Result

Before

[axia@devvm30969.cln0 ~]$ curl http://localhost:20001/v1/responses   -H "Content-Type: application/json"   -N   -d '{
    "model": "/data/users/axia/checkpoints/gpt-oss-120b",
    "input": [
        {
            "role": "system",
            "content": "You are a helpful assistant."
        },
        {
            "role": "user",
            "content": "Multiply 234.234 * 2342.123."
        }
    ],
    "temperature": 0.7,
    "reasoning": {
        "effort": "medium",
        "summary": null
    },
    "stream": true
}' | jq

{
  "response": {
    "id": "resp_d0aa5a27926f4e87aef046739cbe30c0",
    "created_at": 1757365874.0,
    "error": null,
    "incomplete_details": null,
    "instructions": null,
    "metadata": null,
    "model": "/data/users/axia/checkpoints/gpt-oss-120b",
    "object": "response",
    "output": [],
    "parallel_tool_calls": true,
    "temperature": 0.7,
    "tool_choice": "auto",
    "tools": [],
    "top_p": 1.0,
    "background": false,
    "conversation": null,
    "max_output_tokens": 130977,
    "max_tool_calls": null,
    "previous_response_id": null,
    "prompt": null,
    "prompt_cache_key": null,
    "reasoning": {
      "effort": "medium",
      "generate_summary": null,
      "summary": null
    },
    "safety_identifier": null,
    "service_tier": "auto",
    "status": "completed",
    "text": null,
    "top_logprobs": null,
    "truncation": "disabled",
    "usage": {
      "input_tokens": 95,
      "input_tokens_details": {
        "cached_tokens": 80
      },
      "output_tokens": 706,
      "output_tokens_details": {
        "reasoning_tokens": 668,
        "tool_output_tokens": 0
      },
      "total_tokens": 801
    },
    "user": null
  },
  "sequence_number": 706,
  "type": "response.completed"
}

^ note in this final response, output is an empty array. This is not what we want.

After:

{
  "id": "resp_c538e484fa114961b45cec59d0244673",
  "created_at": 1757437205,
  "instructions": null,
  "metadata": null,
  "model": "/data/users/axia/checkpoints/gpt-oss-120b",
  "object": "response",
  "output": [
    {
      "id": "rs_232ea61291404b888e705fd0c5d13f5b",
      "summary": [],
      "type": "reasoning",
      "content": [
        {
          "text": "User asks: \"Write a short sentence about a robot learning to dance.\" Straightforward. Provide a short sentence.",
          "type": "reasoning_text"
        }
      ],
      "encrypted_content": null,
      "status": null
    },
    {
      "id": "msg_1c136508c9844941be70926b34681538",
      "content": [
        {
          "annotations": [],
          "text": "The robot twirled its metal limbs, discovering rhythm with every clank as it learned to dance.",
          "type": "output_text",
          "logprobs": null
        }
      ],
      "role": "assistant",
      "status": "completed",
      "type": "message"
    }
  ],
  "parallel_tool_calls": true,
  "temperature": 0.7,
  "tool_choice": "auto",
  "tools": [],
  "top_p": 1.0,
  "background": false,
  "max_output_tokens": 256,
  "max_tool_calls": null,
  "previous_response_id": null,
  "prompt": null,
  "reasoning": {
    "effort": "medium",
    "generate_summary": null,
    "summary": null
  },
  "service_tier": "auto",
  "status": "completed",
  "text": null,
  "top_logprobs": null,
  "truncation": "disabled",
  "usage": {
    "input_tokens": 88,
    "input_tokens_details": {
      "cached_tokens": 0
    },
    "output_tokens": 54,
    "output_tokens_details": {
      "reasoning_tokens": 24,
      "tool_output_tokens": 0
    },
    "total_tokens": 142
  },
  "user": null
}

---

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• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan, such as providing test command.
• The test results, such as pasting the results comparison before and after, or e2e results
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[qandrew]

@aarnphm @DarkLight1337 @robertgshaw2-redhat @simon-mo this PR is ready for review :)

[heheda12345]

Also CC @yeqcharlotte

[lacora]

LG! saw you define StreamingResponsesResponse in later PR, do we plan on update BaseModel in this diff as well

[qandrew]

LG! saw you define StreamingResponsesResponse in later PR, do we plan on update BaseModel in this diff as well

I have a follow up PR here: #24556.
I wanted to stack the PRs but it seems like I can't do it with forked repos, this is the relevant commit to replace BaseModel with StreamingResponses types: 7c642b0

i thought it would be easier for review to split them into 2 PRs but could combine them too :)

[chaunceyjiang]

This PR addresses three different changes. I recommend splitting it into multiple separate PRs. This PR should focus only on fixing the issue where the output of the last event is empty.

[yeqcharlotte]

let's also add a unit test covering this behavior. the test can be constructed similar to https://github.com/vllm-project/vllm/blob/main/tests/entrypoints/test_context.py#L313

[chaunceyjiang]

+1

[qandrew]

ty for the suggestion, just added

[qandrew]

ready for re-review @chaunceyjiang

[chaunceyjiang]

Thanks~