Fix Responses API background=true + stream=true panic (#1945)

[glaziermag]

Fixes #1945
(Alternative to closed PR #1989 which aggressively disables streams).

Description

This fixes a hard background thread panic when hitting the /v1/responses endpoint with background=true and stream=true.

The endpoint spawned a background Tokio worker which polled its async mpsc receiver using a naive single-shot match bg_rx.recv().await. When stream=true was provided, the underlying core text pipeline correctly emitted Response::Chunk(...) payloads. Because the background receiver wasn't looping, it instantly aborted with Unexpected response type upon encountering the first stream chunk.

This PR wraps the receiver in a while let loop to sequentially bypass stream events in the background while accurately preserving terminal Done, ModelError, or ValidationError states.

Before vs. After Ground Truth

Before Logs (Failing Baseline)

$ curl -s -X POST http://localhost:1234/v1/responses \
  -H "Content-Type: application/json" \
  -d '{ "model": "hf-internal-testing/tiny-random-LlamaForCausalLM", "background": true, "stream": true, "input": "Hello" }'

# [GET /v1/responses/... 5 seconds later]
$ curl -s -X GET "http://localhost:1234/v1/responses/resp_10d61cee-e68f-4963-b049-048ea57caed8"
{"id":"resp_10d61cee-e68f-4963-b049-048ea57caed8","object":"response","created_at":1775517077,"model":"hf-internal-testing/tiny-random-LlamaForCausalLM","status":"failed","output":[],"error":{"type":"unknown_error","message":"Unexpected response type"}}

After Logs (Graceful Handling)

To prove the core engine correctly bypasses chunks and accurately digests terminal boundaries, I intentionally triggered an internal dimension bounds assertion in the testing sandbox.

$ curl -s -X POST http://localhost:1234/v1/responses \
  -H "Content-Type: application/json" \
  -d '{ "model": "hf-internal-testing/tiny-random-LlamaForCausalLM", "background": true, "stream": true, "input": "Hello" }'

# [GET /v1/responses/... 5 seconds later]
$ curl -s -X GET "http://localhost:1234/v1/responses/resp_c9d1fff5-ded1-4b78-b25b-b462706b3895"
{"id":"resp_c9d1fff5-ded1-4b78-b25b-b462706b3895","object":"response","created_at":1775517461,"model":"hf-internal-testing/tiny-random-LlamaForCausalLM","status":"failed","output":[],"error":{"type":"model_error","message":"narrow invalid args start + len > dim_len: [2048, 2], dim: 0, start: 2048, len:1"}}