Summary:
- replace the `sse_completed` fixture and related JSON template with
direct `responses::ev_completed` payload builders
- cascade the new SSE helpers through all affected core tests for
consistency and clarity
- remove legacy fixtures that were no longer needed once the helpers are
in place
Testing:
- Not run (not requested)
seeing issues with azure after default-enabling web search: #10071,
#10257.
need to work with azure to fix api-side, for now turning off
default-enable of web_search for azure.
diff is big because i moved logic to reuse