Every /v1/responses spend log asked its worker to flush the queue right away so a
chained previous_response_id could find the row. Only the chat-completions bridge
reads that row. Native Responses providers hold the conversation upstream, so their
rows now wait for the batch write like chat rows do
Co-authored-by: devin-ai-integration[bot] <158243242+devin-ai-integration[bot]@users.noreply.github.com>
Backport of #47614 to stable/1.105.x.
Cherry-picked from 423362bab2 (main).