Fix flaky test tests/test_db_async.py::test_a_request_burst_leaves_background_work_a_connection

The merge lane saw `tests/test_db_async.py::test_a_request_burst_leaves_background_work_a_connection` fail and then pass on a rerun of the same tree. - Test: `tests/test_db_async.py::test_a_request_burst_leaves_background_work_a_connection` - Tree: `8ec0fd191b9abf197338a19bc0d1e6adbaf5820c` - Lane task: 13210 - Flake record: 01a1a137-958f-799a-b773-11e8a9c7fd42 Make it deterministic; do not delete it unless it tests nothing.

Made the request-burst test deterministic: it waits on observed pool state instead of fixed sleeps and a 1 s timing bound. 27/27 pass, mutation caught, quick gate green. PR #7849 queued in the lane. Memory: none applied.