How does C section birth/NICU get billed?

My wife and I recently had a child via C section and was in NICU for 12 days. My wife is under my insurance plan, and I added my baby to the plan after birth.

Question: I’m assuming since we went to the NICU, the charges are high. Will it all get treated as paying towards my wife’s out of pocket maximum, or would they try to apply both my wife’s and baby boys out of pocket maximum? For my plan it’s $3,300 OOPM for individual and $6,600 for family, so I’m trying to determine how much to shift to my checking to pay.

I’m assuming the C section goes towards my wife’s individual OOPM and the NICU goes towards my baby’s individual OOPM… and thus I should expect to pay 6,600? Looking through documents on my insurance website, it’s not clear.