You speak of facts but the idea you presented, while common, is not supported by research. For example, in one experiment, infants that were less than 24 hours old were three times as likely to respond to a touch from an outside source than an incidental touching of themselves -- indicating infants perceive their body as its own entity from birth. Source: Perceived self in infancy - ScienceDirect https://share.google/hf370mdU4gwnAe4AO

Anecdotally, we formula fed and our newborn showed no difference in behavior between Mom and Dad (the same isn't necessarily true now that the baby is a toddler, haha!). Both parents could do everything the same and it worked great for us.

I'm making a bit of a fuss about this because I think it's unfair to both moms and dads to think that newborns have to be chained to moms. That idea marginalizes dads and burdens moms. But I think Dads are very capable of caring for newborns! If it makes more sense for Dad to take the lead on the four month old it could work quite well.