I was able to get the more information about your ask.
Best place to look at job executions/related details are in the jobs.job_executions view in your Jobs DB for the agent - jobs.job_executions (Azure Elastic Jobs) (Transact-SQL) - SQL Server | Microsoft Learn. lifecycle and last_message columns in that view may give some clues if there was any error coming from your target database(s).
It is possible that your SP executions at the target database are waiting/deadlocking on other activities on that table. Job Agent just kicks off your script executions at the target databases and waits for them to come back. So, the delay/any blockage should be coming from the target database.
I hope that helps
Regards,
Oury