As BR pointed out. A deleted book removes BOTH the book and the DB Entry in the Library.
Using the OS (backup restore) can't make the DB entry and partially damages the Library integrity.
Always ADD these kinds of
corrections BACK thru the normal
Add Books. Unless you have caused Calibre to update the books EMBEDDED metadata, that may be stale.
If your backup
maintains the Library folder structure info, there should be a companion
metadata.opf and
cover.jpg
Open that folder and DRAG
only the OPF into Calibre Library view (A drag and Drop Add), That will make all the DB entries that were current at the time of deletion and bring the book and cover back.