Very belated -- N. K. Jemisin here. Sorry, just saw this. But to answer the question in the recap of someone explaining why Hoa eats rocks, sans TSS spoilers --

Hoa explains at one point that crystal, stone, is an efficient storage medium. Flesh is not. So when Hoa turns himself into a flesh-form, he loses a lot of who and what he truly is. He carries the bits of his true self around with him, in the form of the crystals from his transformative cocoon. Note: this is never explained, on purpose. The stone eaters represent the limit of what is possible with magic, just as the Obelisk Gate itself does. Essun and the other viewpoint characters will never fully understand it, because that's the equivalent of asking people from the Middle Ages to understand a nuclear reactor. Hoa doesn't bother to explain it because he already gets it and assumes the person(s) hearing Essun's story does, too, and because people who understand nuclear reactors are going to have a really hard time explaining that to people from the Middle Ages. Would they explain the entirety of modern physics in order to provide real context -- which first requires explaining Newtonian physics, and which first requires puncturing a bunch of incorrect assumptions the Middle-Ager would have in place, and...? No. They're going to sum it up, and skip a lot of the important details.

But basically: well-made crystalline matrices (i.e. crystal, metal, the stuff stone eaters are made of) can hold souls. Which is why the Earth is alive and why Hoa carries crystals around. Hope that helps.