Fix flaky test tests/support_agent/test_support_entity_tools.py::test_every_new_tool_leaves_the_database_unchanged_but_its_marked_read

The merge lane saw `tests/support_agent/test_support_entity_tools.py::test_every_new_tool_leaves_the_database_unchanged_but_its_marked_read` fail and then pass on a rerun of the same tree. - Test: `tests/support_agent/test_support_entity_tools.py::test_every_new_tool_leaves_the_database_unchanged_but_its_marked_read` - Tree: `f6e4d75b9b43a43785939cbd932a381c53a63b4d` - Lane task: 12965 - Flake record: 01a19e97-4f82-7e21-aa37-c7d0df0e3702 Make it deterministic; do not delete it unless it tests nothing.

Deflaked the support write recorder: it is now scoped to the test's own context instead of hearing every thread on the global engines, and a fixed sleep is now a wait for the marked reads to land. Added a regression test. Quick gate passed; support_agent 303 passed. PR #7809 queued to the merge lane. Memory: none applied.