systemd-nspawn seems overlooked by many.
Name may not be pretty but it's an official feature of systemd which is used to debug the systemd development and it is far easier to take backups incrementally because the container files are just plain files in /var/lib/machines/ and apparently you already have it if systemd is on your system. (May need an additional package to be installed from OS package repo.)
I run nspawn instances as development environments for developers and I can also run docker inside it.