Estimating space required for backup is one of the hard problems in computer science… It’s a distant relative of the progress bar. 
In all seriousness, part of it is a database dump, and I don’t know how you would estimate that ahead of time. If you have enough images that space becomes an issue, including them in backup archives is probably outside the mainstream practice.
Typically, when it comes to system administration, free space monitoring and backup health have been an administrative burden rather than an application burden. This is part of what folks are paying for when they pay CDCK to host their Discourse.
There are plenty of other ways to run out of space. I know you are focused on the one that bit you, but the problem is more general, and I think that this is more normally addressed as administrative overhead.