I think Peridot’s main job was being a ‘certified Kindergartener’. Checking on the Cluster was a recent mission assigned to her (Why and how she got assigned is another question). When we see Peridot doing work involving the Cluster, she’s clinical, if a little bored.
When she talks about Kindergartens, however, she gets excited. She brings it up as part of her qualifications to lead the drill project; she’s cheerful when she examines Amethyst’s hole; and it’s the Kindergartens she mentions first when she sees the colonization plan for Earth.
Peridot is proud of this; no doubt it’s important to Gemkind - it’s propagating the species. She’s at least partly responsible for countless ‘births’ and lives. It’s her doing her part for Homeworld. And it’s why she ends up defecting to the Crystal Gems, believing Earth’s potential for creating new Gems is too important to be destroyed by the Cluster.
Most importantly, she apparently has discovered ways to have Kindergartens and Gem colonies exist on Earth without destroying the ecosystem. That’s huge.
(To Yellow Diamond) I’d like to tell you some plans I came up with to utilize a planet without disrupting the local–
The Kindergartens have been a huge source of shame for the Crystal Gems. We’ve seen how dead the place looks, how much they regretted it even existed, and everything they’ve been doing in the past few millennia has been to atone for it. I’m certain that Rose Quartz with her plant powers tried to find ways to fix the damage, but like with the corrupted gems, she couldn’t find a way.
But with Peridot here, Peridot the modern Gem with experience in building Kindergartens, surely using advanced methods developed by Homeworld over the thousands of years, Peridot with all that expertise, believing she can use Earth without damaging it…
What if eventually in the show, Peridot and the Crystal Gems find a way to bring life back to the Kindergartens? We’re no where near that point yet, but I can’t help thinking that remark is possibly foreshadowing.
The new episode supports the 'Rose is Pink Diamond' theory:
When Steven and peridot are at the kindergarten; Peridot mentions that it must’ve looked better when Steven was created. When Steven says he doesn’t understand-peridot says: “You’re a Quartz, right? So you were forged here.”
Quartz isn’t a type of homeworld gem. It’s an earth gem. But Rose is clearly stated to have come from homeworld (constantly making references to her betraying her home and missing her home; so she isn’t an earth gem).
So Rose is Pink Diamond; and when she betrayed her people, she took a new name: one to symbolize her powers of nature and the place she gave up everything for: Rose Quartz. A Quartz-which the homeworld was happy to call her that so they could strip her title and make it look like just an enemy of earth.