Fix flaky test tests/test_background_on_async_pool.py::test_lease_drains_fan_out_plans_every_node_off_the_loop_on_the_async_pool

The merge lane saw `tests/test_background_on_async_pool.py::test_lease_drains_fan_out_plans_every_node_off_the_loop_on_the_async_pool` fail and then pass on a rerun of the same tree. - Test: `tests/test_background_on_async_pool.py::test_lease_drains_fan_out_plans_every_node_off_the_loop_on_the_async_pool` - Tree: `e5321c7e607828276c2411c153b443d837a6cabd` - Lane task: 13177 - Flake record: 01a1a0de-58bf-7a89-881a-0dfd9ec22172 Make it deterministic; do not delete it unless it tests nothing.

Fixed the flake at its root: a race in db_async.sync_bind() lazily building the bridge. Added a double-checked lock and a test that forces the race (it fails on old code). Quick gate green, file 5/5 green, both review lanes passed. PR #7837 queued to the lane; deploy not yet watched (it follows the lane's merge). Memory: none applied.