What in the world is going on with my coolant?

There are a ton of good replies and I appreciate all of them. To my knowledge, the cap is original to the car. Oil looks normal and the head gasket was recently replaced. The water pump has always looked a bit crusty, but the gasket is still holding strong. Only a passing thought, though. I never gave the pump serious consideration until now. Shade tree mechanic in training, here. Getting a pressure test may be my first try; putt putting around town is still safe and practical so I may just run by the radiator shop and see if they can check it out. My next step may be taking it out, replacing the water pump (again, it’s looking rough from the exterior) and flushing it with vinegar. I’ve heard from some friends that may be worth a shot. From there, if there’s no luck, I may double check the head gasket. If that is no use, I’ll see about upgrading the rad and perhaps repairing the old. What do we think?

Flushing with chemicals is a last resort IMO.

Make a stop at an auto parts store and buy or borrow (you pay, then get a refund when you return it - but they give you a "house" one) a pressure tester. Takes 5 mins or less. No need to drive the car anywhere, unless risking a tow is somehow fun?

The tester comes with adapters. You can Secure it to the radiator opening, and pressurize the system. If it holds, you're fine. Next test the cap: same story. If either fails to hold pressure, then you can move to the next step. I'd replace the cap either way.

If, and only if your rad fails to hold pressure, you can look or listen for where water is dripping or gurgling to help figure out what needs fixed.