[john70t]

There is probably a galvanized<--->copper pipe coupling on the output pipe of the water heater.

(Notice I didn't say "hot water heater" because I assume you don't have rooftop solar pre-heaters. Hah!)

These can go bad, and need to be replaced with a special one to prevent corrosion.
A buddy noticed mine was bad and replaced it. The old one was held together with rust with only a few threads left.
If you have one of those USB mini snake cameras you could check out the pipes from inside.


You also might want to turn off the main, drain a bit from the lowest point in the house, usually the basement tub sink, then pull the shower cartridge and blow it out again. There might be stuff floating around again. Water does that.

Any turning rubber gasket wants to be re-installed with a slathering of plumber's lube/silicone grease.