If the cord is still pulsating then blood is still being pumped to the baby. The difference between immediate clamping and delayed clamping averages 92ml. Which is a lot for a baby, extra oxygen carrying capacity, more iron. But certainly if it’s already breathing, the risk is reduced.
Unfortunately, they do break waters, just to speed things up. Even if labour is proceeding quite normally. And I know one mother last week who was given the epidural just before birth. She kept telling them, but no, the tap went in, the anaesthetic administered and a baby produced thirty seconds later. The negligent staff refused to check how far advanced she was before proceeding.
