Nope:
Different devices have different books. No need to worry about syncing
For most cases, I remove books from the DEVICE (

never, from the Library

) as soon as I have updated the reading status (done date) column, in Calibre.
Backups (full Libraries) are done in multiple places. One is a clone of the Main (desktop) onto my Laptop (grab and go in case of a California disaster). Then there is the NAS And a USB hard drive