Experimental proof for if a d.c. electric current inside a naked wire is being influenced by an external electrostatic field?

Question

For example a d.c. electric current carrying naked wire inserted inside the electrostatic field between the two plates of a vacuum capacitor and with the wire not touching the two plates of the capacitor. Let's assume a straight segment of the wire is parallel to the electrostatic field of the capacitor but the electric field of the current inside the wire which we know by theory in this case is Ew≠0 is antiparallel to the electrostatic field of the fully charged capacitor Ec. (i.e. we assume the capacitor is ideal and has no dielectric leakage due a perfect vacuum).

We assume the steady voltage source powering the wire is positioned outside the electrostatic field of the capacitor Ec, far away.

For Ecw (induced Ec field inside wire) =-Ew by superposition will the electric current inside this wire segment nullified and therefore no current is flowing through the wire connected to the voltage source? The capacitor is fully charged by a second different steady voltage source.

There are contradicting theoretical answers in two different pse questions asking actually the same core question:

Effect of an external electric field on a electric current

If a current flows through a wire connecting two poles of a battery, how high an external voltage must I apply to stop the current flowing?

My interest is if this is actually experimentally resolved?

Note: As far as I know a d.c. electric current carrying wire is electrostatic neutral on its surface there is no charge build up on its surface and there is no any opposing surface field (i.e. no electrostatic equilibrium) that could prevent penetration of the Ec capacitor field inside the wire and therefore influencing its current due superposition with the existing Ew second electric field.

Answer 1

Not at all in classical physics, assuming the wire is made of a simple conducting medium.

Very little if correction to solid state physics is taken into account: The charge density within a (nanometers) thin layer near the conductor surface will change due to bound charges. They can influence conductivity especially for high-frequency currents.

Still the effect will likely be negligible in bulk metal, but it could be measurable if the wire was made of semiconductor or (evaporated) metal film of sub-nanometric thickness.