I cannot find any reliable sources that state Jesus was born in any manner than through the birth canal (the supernatural character being that Mary was protected from injury). Saint Luke himself says simply that Jesus was born. I am on mobile, so please excuse any typos.
The 1910 encyclopedia seems to concur. This suggests to me that alternative birth theories are simply a trend. Such trends have come and gone. Early writings suggest that such trends have existed since within the early days of Christianity.
I watched the video, I believe the Tim Staple one, and he simply says it is a church teaching that the birth had a supernatural character, but he does not elaborate to say that the church believes Christ divined himself out of Mary. The Lateran Council only requires belief that Mary was uninjured, which is no small feat!
This discussion crosses several different points. One is simply fixating on the retoric used, another is outdated medical beliefs. The statement that Mary was a virgin before, during, and after the birth use a trinitary formula. This allows parralel construction with many Christian prayers. For example: Glory to the Father as it was, is now, and forever shall be. The formula emphasizes the eternal nature of God’s glory; it’s use with Mary emphasizes the purpetuity of her virginity.
The middle part is then conflated with Mary’s preservation from suffering the pains if childbirth. It presupposes a “physical virginity”, which is discredited scientifically. There is simply no way to “inspect” a woman to see if she is virgin. Not to get to gross, but women have even been able to give birth with their Hyman intact!
Thus, some authors, including the highest church authorities, used the language of the best physiological knowledge to emphasize Mary’s purity. That “physical virginity” is today known to not be detectable does not detract from Mary’s grace. We must simply find modern language to describe her grace!
In conclusion, we believe Mary to be born full of grace, and every moment of her life to be blessed. As the second Eve, being free of original sin, she experienced no pain during her child birth, and experienced no injury. She experienced ordinary natural changes to her body to accommodate her pregnancy. Language, culture, and knowledge of the anatomy evolve, and metaphor and descriptions from the past may no longer have meaning to modern ears. We must open the windows and breath fresh air into eternal truths in order to spread the Gospel.