Ohm's law tells us that current density $\vec{J}$is proportional to electric field $\vec{E}$. But from my last post  https://physics.stackexchange.com/questions/734379/working-of-battery-in-circuit?noredirect=1#comment1643041_734379

As well as this blog 
https://physicsteacher.blog/2022/07/07/explaining-current-flow-in-conductors-part-one/

a comment introduced me to the concept that it is instead the surface charge density that created the electric field and help in current conduction. So which electric field is the $\vec{E}$ in $\vec{J}=\sigma \vec{E}$ here? Is it of the surface charge densities of the wire pr of the battery? Or is the electric fields inside the wire due to the surface charges same as that of the battery? Kindly enlighten me with the proper concept.