If my VMs can't easily be run on any host from backup they tend to be quite useless at the most critical of times.
As a light user of virtualbox, I get the impression using anything but the gui is really hard compared to other virtualization tools.
For instance, auto-starting raw-disk vms at boot on windows is a pain, and hyper-v is free. Its only real downside is lack of gui support for linux guests.
Similarly, you need to stand up separate backup infrastructures for your desktop and virtualbox, or you will be told "you're doing it wrong" when you try to restore.
I guess I could try to write a script to get a crash-consistent export of running virtualbox vms, but the host file system (btrfs, zfs, etc) already does an adequate job of that, so this is just useless administrative overhead and disk space waste from my point of view.
Anyway, when win8 came out, virtualbox couldn't handle the new start menu, and windows guest vdi was my only remaining use case for it at the time.
It is a shame, VirtualBox was my go-to vm solution for years, specifically for its debian/ubuntu host support (unlike vmware) and good desktop guest support (unlike all the other options).
I've used VBoxManage to create, manage and control VMs on remote headless hosts. And work with VRDC desktops. Easy.
Backup/restore of host system should have nothing to do with VirtualBox. It's just files. But then, I use Debian hosts. For backups, I tend to use LUKS-encrypted SSDs via USB, and just copt the full VM folder. Works perfectly.
IME, you can't.