fix(agent): task completion safety net — stop tasks sticking at Running

Implements fixes 1-3 of plans/2026-07-11-task-completion-safety-net.md.
Confirmed live that 50/50 production sessions never reached a terminal
status because the model almost never calls complete_task, even for
trivial single-tool Q&A turns SOUL.md explicitly calls out as needing it.

- Inline safety net (agent.go): a session that never called set_goal never
  framed itself as a structured task, so its first plain-text turn-end IS
  the task ending — auto-complete it there instead of leaving status stuck
  at its creation default forever.
- Idle sweep (continue.go, new completion_nudges column): goal-bearing
  sessions that stall get one nudge, then auto-close with outcome=partial
  if the nudge goes unanswered, mirroring the pattern resumeSession already
  uses for a different stuck-session failure mode.

Fix 4 (backfill of the 50 already-stuck live sessions) is deliberately
separate — deferred until this is deployed and verified live, per the
plan's implementation order.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

cmd/nomos/continue.go

@@ -32,6 +32,71 @@ func extractExecutionIDs(toolResult string) []uuid.UUID {
 	return out
 }
 
+// idleTaskThreshold is how long a goal-bearing session can sit non-terminal
+// with no activity before the idle sweep nudges it, per
+// plans/2026-07-11-task-completion-safety-net.md. Arbitrary starting point,
+// not measured against real task durations — long enough that it won't fire
+// mid-turn, short enough the board doesn't lie for hours.
+const idleTaskThreshold = 15 * time.Minute
+
+// runIdleSweepWorker is the safety net for case 2 of
+// plans/2026-07-11-task-completion-safety-net.md: sessions that called
+// set_goal (so the inline safety net in agent.go correctly left them alone,
+// since they framed themselves as a real task) but then stalled without
+// ever calling complete_task. Coarser than runContinuationWorker's 4s tick
+// since "gone idle" is a much slower signal than "an execution just
+// finished." Blocks until ctx is cancelled.
+func (a *agent) runIdleSweepWorker(ctx context.Context) {
+	if a.store == nil {
+		slog.Warn("nomos: idle sweep worker disabled (no store)")
+		return
+	}
+	slog.Info("nomos: idle sweep worker started")
+	ticker := time.NewTicker(5 * time.Minute)
+	defer ticker.Stop()
+	for {
+		select {
+		case <-ctx.Done():
+			return
+		case <-ticker.C:
+			a.processIdleSweep(ctx)
+		}
+	}
+}
+
+// processIdleSweep nudges a stalled goal-bearing session once; if it's still
+// non-terminal on the NEXT sweep (meaning the nudge itself went unanswered,
+// not just that the model is still working), auto-closes it with a
+// visible "auto-closed" outcome instead of leaving it stuck forever — same
+// reasoning resumeSession already applies below for a different failure
+// mode (a resume that produces no response at all).
+func (a *agent) processIdleSweep(ctx context.Context) {
+	stale := a.store.staleGoalSessions(ctx, idleTaskThreshold, 5)
+	for _, s := range stale {
+		s := s
+		if s.CompletionNudges == 0 {
+			safego.Go("nomos:idle-nudge:"+s.ID, func() {
+				if err := a.store.bumpCompletionNudge(ctx, s.ID); err != nil {
+					slog.Error("nomos: idle nudge bump failed", "session", s.ID, "error", err)
+					return
+				}
+				note := fmt.Sprintf("[System: this task ('%s') has been idle for %s with no complete_task call. "+
+					"If the goal is done (or can't be completed), call complete_task now with the outcome and a "+
+					"one-line summary. If you're still genuinely working through the plan, ignore this and continue.]",
+					s.Goal, idleTaskThreshold)
+				a.resumeSession(ctx, s.ID, note)
+			})
+			continue
+		}
+		safego.Go("nomos:idle-autoclose:"+s.ID, func() {
+			summary := fmt.Sprintf("Auto-closed after %s idle with no response to a completion nudge.", idleTaskThreshold)
+			if err := a.store.completeTask(ctx, s.ID, "partial", summary); err != nil {
+				slog.Error("nomos: idle auto-close failed", "session", s.ID, "error", err)
+			}
+		})
+	}
+}
+
 // runContinuationWorker is the event loop that replaces the human typing
 // "continue". It polls for gated executions that (a) were initiated by a chat
 // session and (b) have just finished, and — while that agent has an open assent