A handler session only learned the chain was capped when handoff_list_handler
threw at the end of its work, stranding open tasks. The round count already
lived in HandoffRoundTracker the whole time -- it just never reached the
brief. InteractiveLaunchSpecService now reads HandoffRoundTracker.GetState
(read-only, doesn't advance the round) and renders round N of MaxHandoffs
plus the remaining count into the handoff brief, replacing the old one-line
finalNote. The rejection error also names the next action (start a new
handler run) instead of just failing.