The 5 primary manifestations of Prakriti (Adi-Shakti) are Goddesses Radha, Durga, Lakshmi, Saraswati and Savitri. All women in this universe have emerged from a part of Prakriti [Ref: Devi Bhagavatam 9.1.1, 9.1.96-143].
When there is a birth of a girl child in the house, don't we say Goddess Lakshmi has taken birth in our family?
Coming to Draupadi's birth.
Yes many many Scriptures do, mostly the verses are lost but some are available and trackable in current Editions of Garud Puran, Skanda Puran, Padma Puran, Bhavishya Puran as well as Valmiki Ramayan and Balitha Shuktam