If I were writing the story I would say that they don’t. Accidentally releasing a trapped or bound demon is a common theme and I don’t want to argue about what it breathed and ate for a thousand years before it was set free. (And where did it poop?) But I don’t know what the rules actually say. Constructs explicitly don’t need to breathe so does everything that doesn’t have that statement in its description need to breathe? I suppose so, in which case you’re correct.
If I were writing the story I would say that they don’t. Accidentally releasing a trapped or bound demon is a common theme and I don’t want to argue about what it breathed and ate for a thousand years before it was set free. (And where did it poop?) But I don’t know what the rules actually say. Constructs explicitly don’t need to breathe so does everything that doesn’t have that statement in its description need to breathe? I suppose so, in which case you’re correct.