I don’t know where the line is because with art restoration you’re actually modifying a physical object. I guess a better comparison would be modifying an arcade cabinet or something.
It’s not the most robust analogy, but I actually really like your comparison to painting restoration; to do it well, one must understand the techniques and materials used in the original (even stuff below the visible surface).
Not a lawyer, but I think the original work is still copyrighted, and that restoration wouldn’t (or certainly shouldn’t) constitute a new artwork. Though now I’m wondering about that terrible Jesus painting restoration from a few years back — it’s certainly different from the original, and whilst it might not seem reasonable to call it a new piece of “art”, it’s certainly inspired a great many people(to make memes)
