Broadcast "answering-idle" as soon as the waiting list becomes empty

Broadcast "answering-idle" as soon as the waiting list becomes empty

That is, as long as the answering phase has been going on for a "while".

This avoids an awkward pause when all active players are done
answering, everybody wants to move on, but the "Move On" button hasn't
appeared yet, (because clients haven't been told yet that the
answering phase is idle).