Suppose an electron outside a wire is moving with the same velocity as the electrons inside, then due to length contraction, there would be excess positive charges per unit area causing attraction of the election towards the wire, and the positive charges moving in this frame of reference with the same velocity of the electrons but in the opposite direction will create a magnetic field that wouldn't affect the electron that is not moving in this frame of reference. Now, if a grounded shield is placed around this wire, the electric field would not penetrate it and therefore there should be no attraction but then why is the electron attracted to the wire in spite of this shield?
In the frame of the now stationary electron you could put a cylindrical shell of conducting material around the wire.
Since the wire has a net charge and has an electric field pointing from it, the conductor, if isolated will redistribute its charge to have an equal and opposite charge on the inside surface of the shell and an equal charge on the outside surface. And the electric field will continue outside just the same as inside.
And the stationary electron outside will feel that electric field. Charges outside a Faraday cage still feel an electric field from the amount of charge inside.
If you try to ground the conducting shell then you are grounding in a frame.
And scalar potential is gauge dependent, and you can pick a gauge for statics, but statics is frame dependent. If you looked at that result of just charge on the inner surface and moved back to the original frame you see an equal and opposite current on that surface and see a moving person saying that to them it looks grounded.
Magnetic fields are not just electric fields in a different frame, that would not explain travelling electromagnetic waves.