Of course there is no connection between potential (or potential
difference) despite the presence of surface charge if the wire is in
equilibrium! See my summary of surface charge in electrostatics.
For the record, the Sommerfeld and Marcus calculations pertained to a coax
cable of long but finite length, held at a DC potential difference. They
show that if the density of surface charge in this situation is linear with
position along the center wire, the field in the wire is uniform. The
connection to our textbook is that we point out that a nonuniformity in the
surface charge can contribute to the field in a wire.
Maybe it cuts no ice, but it is John who speaks of our textbook connecting
charge to potential, not our textbook. As an expert, he interprets it that
way, but in our chapter 19 (fields in circuits) potential and potential
difference don't get mentioned.