I'm not aware of any OOB solutions like that. Below are the possible custom solutions:
Option #1:
Create a custom logger and dump your specific events/details in logs on the following package or your custom code package. You may apply filter for your specific events/topics.
org.apache.sling.commons.scheduler
Scrape logs and integrate it with a tool of your choice like Splunk etc.
Option#2:
Use MBeans and create your own custom dashboard or Integrate it with HealthCheck/Operations dashboard [1]
Check Adobe Experience Manager Help | Creating Adobe Experience Manager Sling Servlets that invoke MBean o...
http://localhost:4502/system/console/jmx > Possibly commons.scheduler.running.jobs or slingCommonsSchedulerHealthCheck or slingJobs or oak (you could raise a ticket and get the exact name)
Option#3:
Raise a ticket and find out if there is any flag available to generate logs for specific time range for /system/console/status-slingscheduler
[1] Operations Dashboard