Follow David’s 2 suggestions. All water is not the same. Most municipal water facilities treat the water to prevent corrosion. Thie add a food grade chemical usually a phosphate. Private well owner’s do not until a problem is identified. You apparently have a problem that needs to be identified. A water softener will not correct a problem such as yours. There are several solutions depending upon what the problem causer is.
I am a chemist, not a plumber, but I do water quality testing as a sideline to my fulltime job doing protein synthesis. Copper turns green when it comes in contact with either a strong oxidizer (like bleach, not chlorine, since bleach is hypochlorite). My bet is that the water is more acidic than to be expected like a pH of 6 or lower. pH testing is one of the simplest to do, so I’d start there.