Just a couple of Quartz headcanons.
Headcanon 1: Quartzes are made to naturally have this very close, tight-knit, family like relationship with each other, which would make sense for gems that are meant to work in groups. That’s why when our Amethyst came out all alone she bonded with the rocks of the kindergarten as if they were her peers (kind of like an orphan duckling imprinting on an innanimate object).
Also it makes Jasper’s case even sadder, because she probably has the same instinct (programming?) in her, but she rejects her peers. Which is related to my second headcanon.
Headcanon 2: I believe Jasper was probably send to the Zoo along with the other Earth quartzes after the war, and it was only afterwards that she was transferred to Yellow Diamond’s court and put into service in Homeworld.
Very flimsy evidence for this headcanon, but in The Return when Lapis tries to protect Steven by saying he’s only a human, Jasper answers:
“I know what a human is” with distate and desinterest. It makes me think she may have been familiar with humans, not only because she was created on Earth, but because of her time at the Zoo. (Let’s remember both Peridot and the Rubies seemed completely ignorant of what a human being is or can do, even Eyeball who was an Era 1 gem that fought in the Gem War on Earth).
No wonder Jasper was so dissapointed to not find Rose Quartz, but she was brought along just to deal with humans, the very same task she thought she had left behind.