I don't know. You (or, at least the medical profession) would say, "nursing mothers" for breastfeeding mothers. (Or, for that matter, animals still feeding their young.) Then there's 'wet nurse'.
But you also employ a 'nurse' for general healthcare - and not just babies. What about someone who is 'nursing' a teenager in hospital? Or is employed as a nurse for an elderly or disabled person?
To me the word has more than one meaning and the context would tell you which sense. I agree that it's generally used by the medical profession as a synonym for breastfeeding, but I would also use it for generally cuddling and soothing baby. So you (and "you" could be male or female) might ask if you could, "Nurse the baby for a bit," meaning that you want to cuddle it.
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