This seems a "junior" job that could be used as a developer training test.
Let's start with the analysis.
1. Are we going to implement only disk usage only in the email, only in the dashboard or both?
2. how could we show it in the email?
3. and in the dashboard?
The backup process is split in 3 steps:
1. pre-backup to dump db and mount backup destination
2. data copy
3. post-backup to clean db dumps and unmount
I'd add an action to the pre-backup phase to "record" somewhere disk usage after mount.
Then, we need to find a way to insert the information in the email report and the dashboard.
Caution: the disk usage on the dashboard is recorded at time of backup, it's not calculated when you login to the dashboard.
Also, we could add the action in the post-backup instead of pre-backup to report disk usage after the backup (maybe is better).
Those are the first things that came to my mind, any other issue I may have forgotten?
Any more hints?