We've seen a character with an escort before -- Sapphire, in the Answer, had an escort of three Rubies.

I kind of got the impression that Jasper was meant to be a different kind of escort. Not like an, "I'm going to serve and protect you" kind of escort, but a, "I'm here to make sure you don't fuck everything up again" kind of escort. Or a supervisor. I don't know. My reasoning is that Jasper doesn't even show up until Peridot has failed multiple times to complete her mission, and the way Peridot says, "Now do you believe I needed an escort?!" makes it sound like Yellow Diamond didn't feel an escort was necessary. Which, combined with Yellow Diamond's overall attitude toward her, suggests that she isn't terribly important, certainly not in the way Sapphire was.

And who screwed this up? Jasper.

Again, I'm not so sure about that. Peridot was supposed to handle the mission by herself first, and it was only after the CG's screwed everything up that Jasper was sent to join her. Jasper did fuck up pretty badly by deciding on a change of plans, but her change of plans also suggests that she was more in charge of the mission than Peridot at that point.

Yellow Diamond seems to just want the Earth destroyed, and how little she considers Earth life, she probably wouldn't find Steven to be very interesting, just another abomination to be destroyed along with the disgusting planet.

Keep in mind, at this point Jasper literally thought Steven was Rose Quartz. I think Yellow Diamond would definitely be interested to find out that the leader of the rebellion was apparently still alive and well.

That said, I agree that she kind of sucks at her job. She seems to make a lot of really impulsive decisions without thinking through the consequences. I get the feeling Yellow Diamond isn't exactly pleased with her, either.

I also agree about the last chance/redemption idea. I don't feel like Jasper would've made a spontaneous decision like that if she didn't feel she had something to prove.