Have you ruled out a dying hot water heater? If not, get two white bowls, fill one with cold and one with only hot water, see if colors match

I doubt that it's bacteria. I expect that it's rust or other buildup on the inside of the water mains which could be very very old in this town. Is it worse when you draw water quickly than when you draw slowly (and don't cause a disturbance in the main)?

It’s more like residue that builds up over time. Every few weeks there’s an orange tint that forms. It scrubs away with a little elbow grease.

It's airborne bacteria called Serratia marcescens. Everyone, everywhere has the issue, it's not a Salem thing. Thrives in damp, feeds on fatty substances in soap and dishwasher detergent (that's why it shows up in dishwasher). It's killed by chlorination in water, but if tap water stands long enough, the chlorine evaporates and it can grow again. That's why, if you leave a glass of tap water by the bedside for a week, it may be slimy inside or even a bit pink when you remember and clean it. In the tub or sink, can be cleaned with bathroom cleaners, but even vinegar solution will do it. It's pretty harmless unless you're immune compromised. Rust can be an issue, but usually it's darker and is difficult to clean and even stains.