Covers the reviewer-requested cases for #98555:
- successful streamed response emits the latest attempt's non-null
first_chunk_at (started_at <= first_chunk_at <= ended_at)
- non-streamed, failed-stream, and partial-stream-stub paths emit None
- a stale timestamp from a prior API call cannot leak into the next
call's post_api_request payload (per-attempt reset in the loop)