Summary

Implements LOBE-8233 — heartbeat tasks now actually heartbeat. Previously LocalTaskScheduler was wired to no callers and QStashTaskScheduler was a TODO; onTopicComplete ran once and stopped.

After this PR, every task with automationMode='heartbeat' self-arms its next run via QStash delayed publish (or LocalScheduler setTimeout in dev). DB is the state authority — every tick re-reads task state and may decide to skip rather than run.

Mechanism (per design doc)

• Re-arm in TaskLifecycleService.onTopicComplete: after the existing terminal/pause logic, schedule the next tick with delay = task.heartbeatInterval. Persist tickMessageId / scheduledAt / consecutiveFailures under tasks.context.scheduler.* (JSONB pocket — no schema migration).
• Failure fuse: 3 consecutive error reasons → stop re-arming and let the urgent error brief surface for human action.
• Skip-when-human-waiting: any unresolved priority='urgent' brief blocks re-arm (covers review max-iter and fuse cases without a new schema column).
• QStashTaskScheduler: thin wrapper over qstashClient.publishJSON({ delay }) + messages.delete(messageId). LocalTaskScheduler already existed, now actually invoked.
• Watchdog cron: /api/workflows/task/watchdog handler reuses TaskModel.findStuckTasks. Cloud schedule registration is left to a one-time runbook (intentionally not auto-registered to avoid duplicate schedules.create).
• Signature verification added to /on-topic-complete, /heartbeat-tick, /watchdog (skipped when QSTASH_CURRENT_SIGNING_KEY is unset, matching existing verifyQStashSignature behavior).

Refactors

• Extracted TaskRunnerService.runTask from the task.run mutation (~180 lines → 14-line wrapper). Both router and tick handler share one runner.
• Moved buildTaskPrompt into @lobechat/prompts with structurally-typed model deps so the prompts package stays free of @lobechat/database imports.

Out of scope (deferred per design doc)

• Tunable per-task fuse threshold (hardcoded 3).
• start/pause/resume/cancel extraction to TaskRunnerService.
• Local-mode auto watchdog setInterval.
• Cloud watchdog cron auto-registration.

Test plan

• bunx vitest run src/server/services/taskScheduler (qstash + local, 19 tests)
• bunx vitest run src/server/services/taskLifecycle (10 re-arm tests covering done / error / fuse / urgent-skip / terminal-skip / non-heartbeat)
• bunx vitest run src/server/routers/lambda/__tests__/integration/task.integration.test.ts (19 tests still pass after task.run thin-wrapper refactor)
• bunx vitest run packages/database src/models/__tests__/{brief,task}.test.ts (77 tests, no regressions)
• bun run type-check clean (only pre-existing .next/dev/types artifact error)
• Cloud (queue-mode) manual verification — set AGENT_RUNTIME_MODE=queue, run a heartbeat task, confirm messageId appears in QStash dashboard and tick fires after heartbeatInterval.
• Cloud watchdog cron registered manually:

  qstashClient.schedules.create({
    destination: '<APP_URL>/api/workflows/task/watchdog',
    cron: '*/5 * * * *',
  });

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