Please see my reply above.
could we see an activity log for all Server Side backups and deletions on that page?
No, those actions will be added to the short (admin) log, where all the other (searchable) admin actions are listed.
We would suggest that when using the backup feature you take special care not to accidentally click on the "Delete All Backups" button, which is next to the "Backup" button. If you are in too much of a hurry, it's possible for the focus of the mouse to slip. Bear in mind also that clicking that button will delete all backups older than one week, but newer backups will remain intact.
Unless something really serious has happened, it's not often that anyone would want to restore to a point a whole week (or more) ago. Consequently, it's not necessary to retain "ten backups" as someone has suggested - ten just happens to be the maximum allowable number.