Hello: I can’t answer your question directly, but possibly can help narrow down the possibilities. I’d take a white bucket and fill it with hot water. Do the same with cold water. Let them both settle and see what’s in the bottom of each. Do you get similar “stuff” in the cold bucket? If so, we know the source is not the heater.
One question: Do you have a recirculation line? If so, this could be letting stuff into the plumbing. 😉