They are saying that judgements of what qualifies as harm is something like a judgement of what is good, or what is right or wrong. That’s not the same thing as evaluating whether something causes pain. You can measure whether something caused pain, sure. (Well, the sort of limitations you mentioned in measuring pain exist, but as you said, they are not a major issue.)

“Harm” isn’t the same thing as “pain”.

I would say that when I bite my finger to make a point, I experience pain, but this doesn’t cause me any suffering nor any harm. If something broke my arm, I claim that this is harm to me. While this (“if my arm were broken, that would be harm to me”) might seem like an obvious statement, and I do claim that it is a fact, not just an opinion, I think I agree that it is a normative claim. It is a claim about what counts as good or bad for me.

I don’t think normative claims (such as “It is immoral to murder someone.”) are empirical claims? (Though I do claim that they at least often have truth values.)