[Engine] serve: report timings on /v1/responses

[pschaub]

Problem and result

/v1/chat/completions returns top-level timings (#107), but /v1/responses (#451) does not, although server.py already computes them for every request. Now the final response.completed / response.incomplete event and the non-streaming reply include the same timings object.

Related discussion

Follow-up to #107 (based on #83) for /v1/responses.

Approach

_with_timings in serve/responses.py copies done["timings"] onto the final event; collect() keeps it on the non-streaming reply. Nothing else changes.

Validation

Passed:

• python -m unittest discover -s serve -t . -p "test_*.py" on this branch (one commit on main e88ee39), Windows 11, Python 3.12: 882 tests OK, 20 skipped. The same command on main e88ee39 without the change: 881 tests OK, 20 skipped.
• The new UsageAndStatus.test_responses fails without the change.
• Live check on main e88ee39 (Windows 11, CUDA): the final event of streamed /v1/responses requests carries timings; without the change it does not.

Failed:
none observed

Not run:

• Linux and macOS.
• The non-streaming /v1/responses reply was checked by the unit test only; the live check used streaming.
• No CUDA, HIP, SYCL or Metal build: the change is Python only.

Limits

response.failed carries no timings.

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Created with Claude Opus 5.5. The result was verified by a human (me) in llama-swap: prompt and decode speeds now show for /v1/responses requests.