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/tasks.go

@@ -266,3 +266,28 @@ func (a *agent) handleTaskTool(ctx context.Context, sessionID, name string, args
 		return nil, false
 	}
 }
+
+// autoCompleteTrivialTask is the case-1 fix from
+// plans/2026-07-11-task-completion-safety-net.md: a session that never
+// called set_goal never framed itself as a structured task, so a turn that
+// ends with a plain-text answer and no further tool calls IS the task
+// ending — but the model consistently skips complete_task for exactly this
+// case (confirmed live: 43/50 production sessions were a single trivial
+// Q&A exchange, none of which ever reached a terminal status). Rather than
+// leave agent_sessions.status stuck at its creation-time default forever,
+// close it out mechanically here: no judgment call needed, since SOUL.md
+// already treats a one-shot answered question as done by definition.
+func (a *agent) autoCompleteTrivialTask(ctx context.Context, sessionID, responseText string) {
+	summary := strings.TrimSpace(responseText)
+	summary = strings.SplitN(summary, "\n", 2)[0] // first line only — the board shows one line
+	const maxLen = 120
+	if len(summary) > maxLen {
+		summary = summary[:maxLen] + "…"
+	}
+	if summary == "" {
+		summary = "Answered without further action needed."
+	}
+	if err := a.store.completeTask(ctx, sessionID, "success", summary); err != nil {
+		slog.Error("nomos: auto-complete trivial task failed", "session", sessionID, "error", err)
+	}
+}