The divergenc of steady current density is zero

$\nabla \bullet \vec{J}=0 $

And, by microscopic Ohm's law $ \vec{J}=\sigma \vec{E} $

If the conductivity is uniform, we can get $\nabla \bullet \vec{J}=\sigma \nabla \bullet \vec{E}=0$.

That is, $\nabla \bullet \vec{E}$

And, by gauss's law ( $\nabla \bullet \vec{E}=\frac{\rho_v}{\epsilon_0}$), $\nabla \bullet \vec{E}$ implies that the volume charge density $\rho_v$ is zero.

But, i can't understand why the charge density is 0. Of course, when current flows in a wire, the positive and negative charges are balanced, so the charge density is 0.

However, if the free charges in the vacuum constitute a steady current (a), then it makes no sense for the charge density to be 0.

What am I misunderstanding? Or does a situation like (a) make no sense?