Gate 1 found the teacher staying silent after a research brief landed.
The SDK only evaluates sendAutomaticallyWhen inside addToolOutput — an
external setMessages (our syncFromServer) updates the UI but never
triggers the continuation. Fix: syncFromServer checks
lastAssistantMessageIsCompleteWithToolCalls and calls sendMessage()
(itself a valid continuation trigger); plus a mount-continuation effect
for the reload case (job fulfilled while no client was open).