Will let you cut & paste to a network drive.
backintime perhaps?
It’s in the AUR. 
pamac build backintime
Disclaimer: I’ve never used it, so I don’t know whether it’ll do what you ask.
It’s in the official repos:
Try backintime, its a great piece of software that i use to backup “/” ( whole System) every night.
Backintime saved my “life” a lot of times! I backup ext4 filesystem to external ext4 USB-drive.
Backup to a filesystem that “knows” Linux rights like rwx… ext4 for example.
With Backintime you can restore single files/folders/whole system
I don’t know if its capable of handling btrfs systems — google!
Good luck and never forget to backup your data!