The idea behind that theory that the woman was one half suggests that prior to the split, it was one being who was half male and half female, not one man from whom woman was created. Also, that being was the one made in the image of God.
It makes some people angry.
Enki and Ninhursag https://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=t.1.1.1&charenc=j
Enki, Sumerian god of water and knowledge, goes around distributing his semen to various goddesses for generations, and attempts to get busy with one who happens to be his great granddaughter, Uttu, after posing as a gardener. Ninhursag, the mother goddess of mountains, says no and takes out the semen from wherever he splashed it, then plants it in the ground. Various fruits, trees, vegetable, grass, plants grow from the place she planted it, and Enki eats them - to know what they are and determine their destiny because that’s what he does as the god of knowledge. No kinkshaming.
Shortly after, Enki feels pain all over his body. Ninhursag asks where it hurts, and it turns out the pain comes from the plants and basically the semen is spreading inside his body. The top of his head hurt, Ninhursag removes the source of the pain which gives birth to a god of vegetation; a lock of hair, his nose, his mouth, throat, arm… give birth to multiple goddesses like Ninkasi goddess of beer, Nanshe goddess of the sea.
And then his rib hurts, and Ninhursag gives birth to Ninti out of it. Ninti translates to lady of life / lady who gives life, but it’s believed that this part is a play on words that would mean lady of the rib. The Eve of Hebrew myth is thought to have been inspired by Ninti.
I don’t know about versions of biblical texts, but the tradition that Eve came from a rib may come from people who were aware that this story was derived from Enki and Ninhursag. This myth involves a garden and stuff associated with the land of Dilmun, which was at some point connected to Eden. Plus Adam as a gardener eating the fruit to gain knowledge. Adam eats the seed of the apple but more like his own seed.
ETA: oh yeah, apparently Ninti “lady of life” literally translates into chavah in Hebrew meaning “to live” or “to give life” which became Havah then Eve. so Eve’s name also carries that play on word with lady rib, except it was lost in translation (I’ll just assume Hebrew for rib is different).
Romance of the Three Kingdoms and Water Margin were also written in the same period (14th to 16th c.) and are also heavy-handed that way. Romance pushes Liu Bei as the perfect Confucianist ruler restoring the Han glory (the same one that ended ultra corrupt and lived in luxury while everyone was dying of starvation from taxes and disasters), while throwing as much shit as possible on Cao Cao the reformer and usurper of the Han, and Water Margin starts with the first half showing a whole bunch of characters suffering from imperial oppression building up a large rebel group, only to turn around and have them say “actually all we ever wanted was to be part of the imperial army, let us beat up that other rebel group led by an evil wicked wizard and die to prove it” in the second half (which is actually the more historical part of it…)
Those are 3 of the 4 greatest classics of Chinese literature.