Hi NAS, this is one solution.
Another (the one I'm looking into now) is to have the setting for the volume that is holding the backups read from the db, then see the free space of that volume.
After the info of free space in the Dashboard is updated, the volume is released.
This will make the information more "live" and accurate, but it will pose the problem of mounting/unmounting the volume every time you access the Dashboard.
I took this into account because in the method you specified, the read is from a file that was created at the moment of the backup, and a lot can change on the target volume from then until the new backup. (files can be added to that volume and space can decrease).
So a more frequent read of that volume's free space seems more logical to me.