Add a Backup() method to the API client

This is a simpler change than my previous one.  It does not try to pull out the common HTTP request code.  In the interest of getting this done sooner, here's a patch with smaller scope.  It stays closer to the original patch from perrito666/voidspace.

Note: I've decided to punt on a full functional test for backup.  It is too heavy a lift for this changeset.  For now we can just rely on the CI tests that we have for backup/restore.
I've cleaned up this whole section.