Any backup program that can do an 'incremental' would do the job.
The 'Calibre' part of the problem is:
Recovering a Library from all those bits and pieces.
You would restore the LAST metadata.db, then you need to find and restore all the Latest versions of New ADDS (inc format conversions) , Edits and create containing folders to hod ne stuff.
Get a External HD like a WD Passport. Fast (USB3 capable), fairly small and lots of room for the Calibre 'Export' archive