Actually, if you defer all your coding decisions to agents, then you're not doing engineering at all. You don't say you're doing "contractor engineering" when you pay some folks to write your app for you. At that point, you are squarely in the management field.

If you're producing a technological artifact and you are ensuring it has certain properties while working within certain constraints, then in my mind you're engineering and it's a question of the degree of rigor. Engineers in the "hard engineering" fields (eg mechanical engineers, civil engineers) a rule don't build the things they design, they spend a lot of time managing/working with contractors.