Is it necessary to make up the 27th day of Ramadan if a woman felt labor pains and the water that precedes childbirth came down on that day, and she did not break her fast until after childbirth at night?

You are not required to make up that day, because the wetness that descends before the separation of the child does not prevent prayer and fasting. Scholars differ regarding its purity and impurity, and whether or not it nullifies ablution. The Malikis and Shafi'is consider it to nullify ablution.