The existing gate test mocks both board reviewers as already-idle, so it never
exercises the spawn -> active -> exit -> idle -> next-tick transition — the
boundary the gate actually guards. Add a real-DB integration test that seeds a
board/coordination task plus the agents the handoff resolves against, dispatches
both reviewers through the real handler (the spawn stub leaves each ACTIVE in
_instances exactly as a real container spawn does), asserts board_review_complete
stays False while either reviewer is active, then marks both idle and runs the
next tick to assert the flag flips True and the formal CEO approval notification
is persisted.
