Yellow Diamond and Jasper
So what exactly is Jasper to Yellow Diamond? I would say that Jasper is her way of remembering Pink Diamond, a living memento of sorts that she can deny being for that specific purpose. Yellow has been hesitant to let her feelings about what happened to Pink show even to herself. When talking with Blue Diamond her real feelings take time to bleed out over the course of her song.
Going off this her deciding to take “our” Jasper makes sense. Jasper’s exceptional power provides Yellow with an excuse to have her around, both to the other Diamonds and more importantly to herself. Jasper’s own feeling regarding Earth would have helped Yellow see Jasper as a kindred spirit as well. Not that she would ever actually tell Jasper this, but it’s there.
Notably she is shown to be protective of Jasper. One of the first things she asks during Peridot’s call was where Jasper was, and the line does specify Jasper not just a nondescript word like escort. She doesn’t pres the matter, but Peridot gave her no reason to believe they were in danger. Further more she specifically sends the rubies to retrieve Jasper afterward, when Peridot’s behavior has called Jasper’s status into question.
I can picture Yellow, during a quiet moment, just sitting and staring at Jasper on some screen and thinking about Pink Diamond. She just silently sits there until her Pearl bring her out of her trance.
Give her a hug…. then run.