I have a theory on Sakura Nanamine's personality and why she acts the way she does. She IS putting others down to get what she wants, but I don't think it's actually in a sociopathic way. LET ME XPLAIN!!!!
With how she pushes everyone away, it gives the illusion that she's a heartless sociopath that would do anything to get her way, but I've noticed she clearly has reactions when shes caught off guard or when something happens that she didnt prepare for. I think she is actually very empathetic but is attempting to isolate herself in order to create the illusion that she doesnt care.
I think shes completely neutral because shes intentionally trying to close herself off from others, but she actually does react when she’s caught off guard.
And I think that plays into how sakura is always dismissive of Natsuhiko because she does care about him but doesnt want him to care about her so that she wont feel conflicted about possibly hurting someone close to her.
Shes closed off in an attempt to distance herself from any possible connections so she doesnt end up standing in her own way of her end goal. And as much as she doesnt WANT to care about anyone, she still ends up caring. In the chapter where Sakura sent Natsuhiko into that alternate dimension hellscape with Nene even though hes on the same side as her, Natsuhiko says “She's like this sometimes. She's oddly hard on me, I guess? Like... She's especially rough with me. Special treatment... Just for me... Could it be love...?” and though this was played out like a bit to introduce the trope of guy who gaf and girl who dgaf I think it counts for something else too. I think shes tried to get rid of him because he’s so unconditionally smitten with her that it poses a problem with her attempt at isolating herself.
Considering the only members of the broadcasting club are her, Natsuhiko, and Tsukasa, that leaves Natsuhiko as pretty much the only person close to her. When Sakura was trying to get them to stop pestering her, Tsukasa and Natsuhiko got very different injuries. It was also portrayed as a bit, but they had both been equally annoying and tsukasa was thoroughly injured while Natsuhiko got a slap on the cheek, and that part was a detail that wasn't referenced in the joke.
And I think her uncharacteristic reaction to Natsuhiko asking her out after she explained the result of her plan to end the world was because Natsuhiko suggested he’d somehow still be around. Based on that, she probably felt some kind of relief at the thought that he’d still be there and she wouldnt have to hurt him to reach her goal.
She has very bluntly rejected him all of the times before this because she didnt want to get any closer with him than she already was with the knowledge that if everything worked out for her, he’d be gone. However, she agreed to go out with him this one time because shes realized there a possibility he might actually live to the day that happens, saying, "Well, if you survive.."
i hope they are happy forever