[nmeta]

I too was intrigued by this and did a quick google search.

I came upon this which I think is a similar (if not the same) reaction as is occurring in OP.

https://thehappyscientist.com/content/simple-electrolysis

And in the final paragraph states that, and I'm loosely plagiarizing here, the negative ions created in an electrolysis reaction are attracted to the positive/live terminal*, and in the presence of chlorine (as in salts found in the potato) the copper (wiring) react to form green copper chloride.

Edit: not battery, but positive/live terminal

[robocat]

The way to remember it is that the negative ions of Chlorine Cl- move towards the positive wire electrode.

At the copper wire of the positive electrode the chlorine reacts with the copper to make green hydrated copper(II) chloride - CuCl2·2H2O - https://en.m.wikipedia.org/wiki/Copper(II)_chloride