Claim idle conversation inputs before publishing queue changes so immediately dispatched messages do not briefly appear as pending. Preserve busy conversation queueing and add a regression assertion for notification ordering.
Validation: 369 focused tests, typecheck, and changed-file lint passed. Full-suite runs timed out with failures in other modules; repository lint reports errors in the existing story-graph demo.
Release note: Fix a brief pending-queue flash when sending a message while the agent is idle.