The list of services and processes running on every component is different. If you need to monitor them, then you should be paying attention to all running services/processes to make sure your infrastructure is fully operational. Here is a good example on what components should be monitored > Backup Infrastructure Summary
and Veeam Backup & Replication Alarms
. Feel free to built something similar with your monitoring system, and if you don't have one, then take a look at Veeam ONE.