There is a related issue for this (as both migrations and backups use the same optimized format):
At this current time I would recommend avoiding using Docker on BTRFS inside LXD if you need to migrate/backup efficiently.
If you use a storage pool driver like dir or lvm for your instance’s root disk, or just as a custom volume passed into the instance for use with the docker directory, then Docker can use overlayfs ontop of ext4 filesystem inside the container which will then be efficiently backed up.