Problem

When the Gateway restarts, overdue isolated agent-turn cron jobs are rescheduled and rerun, even if they already completed successfully (lastRunStatus=ok) within the current schedule window.

This causes:

1. Duplicate messages sent to users (e.g., a 09:10 daily reminder fires again after a 11:00 restart)
2. Users with many cron jobs get flooded with repeated notifications
3. Confusing user experience — they see the same content multiple times

Expected Behavior

On Gateway restart, when evaluating catchup for an overdue cron job:

• If lastRunStatus is ok AND lastRunAt falls within the current schedule window (i.e., the job has already run for this schedule tick) → skip the catchup
• Only rerun jobs that have NOT yet executed for the current tick (e.g., lastRunAt is before the scheduled fire time, or lastRunStatus indicates failure)

Current Behavior

All overdue isolated agent-turn jobs are rescheduled and rerun regardless of whether they already succeeded.

Environment

• OpenClaw version: 2026.6.11
• Platform: macOS (arm64)
• Multiple agents with 5+ cron jobs each