Organic? Yes. Living? Nope…

They are made from wood, metal or stone frames with “root-like cords infused with alchemy” as muscles and covered in armored plates. They don’t sleep, don’t eat, don’t drink, don’t breath and are immune to disease.

Their “living quality” is basically just being sentient and not the dumb mindless constructs formerly build.

The part about getting healed normally is mostly balancing… After all healing in D&D terms is mostly magical so why wouldn’t it apply to a magically created sentient creature? It’s not like magic needs (micro-)biology concepts to work. Sentience being the deciding factor between an object and a creature from a view point of magical theory works, too.

(Funnily enough that’s in fact even consistent with rest of D&D magic where a dead body -at least strictly speaking- stops being a creature and becomes an object the moment the concience/soul/whatever leaves…)