After a gateway restart or websocket reconnect, the UI stays stuck in
processing state because reconnecting clients only replay running status
when a turn is active, never push idle when no turn is running.
Fix _hydrate_after_subscribe to always push goal_status (running with
started_at when turn is active, idle when no turn is running) so the
frontend can reset its processing indicator on reconnect.
Also fix cmd_stop reporting 'No active task to stop' when a task is
actually processing by draining the pending injection queue in addition
to cancelling active tasks. This prevents mid-turn injection deadlocks
and gives accurate task counts.
