I manage a diverse set of backup systems, the only commonality is email notifications, There status being Failed, Success, Success with exceptions and unknown(where the email isn't sent).
Case 1) Expect email from system3@example.net every day, at least once a day.
This would catch those instances where the backup server went offline, internet outage, or another unforeseen issue that prevented the backup from run and send out a notification of success/fail.
Case 2) Backup Ran but failed
The backup ran, but failed, and an email went out stating such event occurred.
Case 3) Backup Success
Great, the thing did what it was suppose to do.
If Case 1 or 2, notify me, if case 3, log for audit
The application would email me on failure, weekly status reports of all events (simple HTML email would suffice, tables with servers, days and status of each day)
Update: strictly looking for email based solutions, template assignments for each email address may be needed to properly parse different backup types, I'll list some systems here: FreePBX, BackupExec, Appassure, WinSCP Scripts, CrushFTP alerts, qnap sync, syncback software, rsync solutions, Classic windows backup, Bash Expect scripts (to log-in and backup routers via ssh/expect), monthly maintenance tasks like battery backup tests, and other unknown items that would give the same 3 options