It’s highly recommended to create a backup of your live and staging site directly before you push the staging site to the production website.
WP Staging stores its data in database tables which are prefixed with the string
It’s important to know that most the free backup plugins do not support custom table prefixes that are created by WP Staging with its default settings. (BackWPup is one plugin that supports this kind of custom tables)
So if you create a backup and your backup plugin does not support these custom wpstg_ tables you need to use the same backup plugin on the staging site again. Then you can create another backup of the staging site. This will provide you two separate backup files that contain the entire file system and the database of each website separately.
For example: If you break the live site and you are going to restore the entire database with the database backup from the live website only this could lead to a deleting of the staging site or it brings the staging site back to an earlier state with lost of your latest modifications.
Make sure to have separate backups of your sites and that they contain all the data you need. Whenever possible create separate backups. One for your staging site, the other one for your live site.