Helloooo

So first of all, Haine is not Shide's biological daughter or anything but he is her guardian. Shide, in his 40s, sort of adopted her most likely after her family died because of the famine.
Haine was copied and "eaten" by Hiruko soon after.

From here on, Haine means shadow Haine/Hiruko:
When Haine grew up, altho not sure what age exactly, she and Shide married (coz that's how they do in the 1700s lol).
They soon had a son who then grew up to be the exact replica of Shide, physique-wise (that's the shadow nature when a shadow and a human interbreed).
Since the son is literally the same as the father, Shide came up with a plan to transfer his memories to his son thus restoring his youth. And he, with Haine's help, did this over and over again until present day. Thus, it is more befitting to say that it is Haine copulating over and over again with her son's body but with Shide's memories lol.

So with the way they did, since og shide was human, Haine copied his memories and instead of printing it using a shadow so he could have a shadow body, she transferred the copied memories to their son so he could still have a human body (that's why his situation is very similar to Hizuru and Ryuunusuke).

Hizuru then did the exact opposite on their first fight. Instead of transferring Ryuunusuke, a copied memory in her, to another human body, she transferred him to Shide's armor, which is basically a mud, to create Ryuunusuke's shadow body (the same way as to how a shadow would birth another shadow).
Then in the next loop, Hizuru did exactly what Haine did to Shide and the body of their sons. Hizuru transferred Ryunosuke to Shinpei.
And Hizuru was able to come up with this plan because of the information they gathered from Dr. Hishigata when they confronted him.

I can't explain much but basically, the way Ryuunusuke was transferred to Shinpei is like the same concept as to how Haine was transferring Shide's memory from one Karikiri to another Karikiri lol

If you're talking about the part before OP song, yes it is anime original (at least what's been shown, the info shared in that scene is still pretty much the same with what was shared in the manga) ^^