I think the implication with that reincarnation bit is that Shio has inherited the same brokenness that made Sato what she was: a psychopath for whom empathy and love almost impossible(hence rejecting her brother the second time) and, more tragically, like Sato, does not even register her own mental state as being abnormal. Being such a young age when this transpires, abnormal mental state(i.e. lacking in empathy) will be her normal.
I think that anything resembling a normal relationship will be beyond both her ability and desire, with the mirror implying that Sato is, was, and always will be, the only relationship that shall ever have meaning for her. With Sato now dead, the memories that Shio has are the only thing remaining of Sato, and the only thing Shio will ever deem precious and are completely part of her.
i honestly don't pick that up at all. Just because one is related by blood doesn't make it a healthy or loving connection. Asahi was broken by his experiences with his dad, and basically 'worshiped' an ideal life of him, his sister, and his mother, his sister attaining a similar purity to Taiyou's ideal of her. This is a big reason she says she is dirty to Taiyou; she's rejecting that role. So of course she rejects her brother. That's also why she sees a younger version of him clinging to the real him; he's basically slowly became another variant of their father.
While Sato did bad things, she really didn't do any of them in front of Shio. Even when Sato admitted to doing bad things, she still worked at protecting Shio. And Shio got a form of love and affection that Sato never learned. i see it as Shio taking the best parts of her relationship with Sato, and learning to live for herself, not to be an idol, or represent purity, or as a burden to others.
Swear ta gods, feels like i'm the only one seeing this from a survivor mindset, having been in similar situations (though not to the extremes of this manga).
Only in manga can the murderer protag get the pass of "well atleast she didn't mutilate people right in front of the loli". The writer should be ashamed.