Work produced by the Australian government is copyrighted
by "the crown". That is the equivalent of government buildings.
They are owned by a subset of the public. An entity called
"the (Australian/American) government".
Public domain software is not owned by a government. It
is owned by the public in its entirety, worldwide.
But again, if you want to say "unowned" instead of "owned
by the globe", that's fine. I don't actually understand any
difference between those two concepts.
With the exception that "unowned" implies that someone
might be able to pick it up and claim ownership under the
principle "finders keepers, losers weepers".