Docker on BTRFS is very buggy and can result in a fully-unusable system, in that it will completely butcher the underlying BTRFS filesystem in such a way that it uses far more disk space than it needs and can get into a state where it cannot even delete any image, requiring one to take drastic actions up to and including reformatting the entire affected BTRFS root file system.
According to the official Docker documentation:
btrfs requires a dedicated block storage device such as a physical disk. This block device must be formatted for Btrfs and mounted into /var/lib/docker/.
In my experience, you will still run into issues even if you use a dedicated partition. No, it seems it requires a standalone