I would tend to label this as personality trait curiosity, though not with absolute certainty. It's kind of a classical example of trait curiosity. "Oh, my child is always asking questions about everything -- what a naturally curious kid."

On the other hand, if someone is always wrecking specific electronic devices you own because they want to know exactly how that works, but they never want to figure out how to make you a better tasting dinner, that might be state curiosity? :)

The lines are perhaps not super clear, though.