You can give your users rights to check if reports have run or jobs are complete without granting full admin rights. Here's how you can do so by using SQLAgentReaderRole in SQL Server.

How to Find All Scheduled Jobs in SQL. Microsoft's SQL Server database software includes a job scheduling system which lets you perform routine business activities such as reporting and database ...

To do this, we’ll use an SQL Server Agent Job. Using SQL Management Studio, create a new SQL Server Agent Job: Fill in the general details and then go to the Steps page to add a couple of steps.