Surface charge on a resistive wire in DC circuit

In a simple DC circuits the charge carriers will drift through the bulk volume of the wire and resistor.

Collisions in the resistor (and also wires) will be converted in heat and effectively transferring battery energy to the resistor and less so to the wire.

There will be net charge accumulation on the surface of the wire and resistor maintaining the electric field through it. This field is present in their interior volume continuously accelerating the charge carriers until they collide (very rapidly actually).

See e.g. does-electricity-flow-on-the-surface-of-a-wire-or-in-the-interior and do-electrons-flow-only-on-the-surface-of-a-wire.

Charges of equal sign repel each other. In conductor, this makes any non-zero charge imbalance to spread out and decrease in magnitude. The stable state in electrostatics and in constant dynamic current (DC) circuits is that all excess charge is on surface of the conductor, the charged particles cannot get farther from each other, because (in common low voltage and low temperature cases) to leave the conductor they would have to overcome quite a high energy barrier. So they stay on the surface.

Electric field in case of DC circuits is given by the Coulomb formula. Since there is current flowing in the conductor, there has to be some electromotive force that maintains it. In ordinary wire in DC circuit the only such force can be the Coulomb electric force of charges in the system.