This one was only ever kind of a mystery. With the airing of Log Date 7 15 2 we concluded that Gems had to consume some kind of life force from a world to create more of their own kind. Heck, right after we first saw the kindergarten in On the Run we figured as much.
Still, it was great to hear the show make it explicit, clearly solving the mystery: in Back to the Kindergarten Peridot explained how “formless, aimless energy” was used to create gems; when the resulting Gems leave the kindergarten, they take that energy (and all of the wonderful things it sustains) with them.
Later in the episode we see it demonstrated: it’s not that the soil in the kindergarten is bad, because the sunflowers die despite fresh soil being brought in. There’s an energy that life needs to exist, but the kindergarten doesn’t have any anymore—the Amethysts that were made in the kindergarten have it now.
It might be possible to nitpick and say that not enough sunlight would reach the sunflowers in the canyon for them to survive, but the intent of the episode is obvious: explaining to the viewer how the kindergarten works. Besides, two things should be kept in mind: Peridot knows a fair bit about plants, and the sunflowers likely shriveled up and died in a single day.
So that means we know for sure now: gems use some kind of life force as a power source. This is what allows a Gem to live for thousands of years without ever needing any sort of energy input (with many apologies to the laws of physics), and this is what keeps the kindergarten so devoid of life even thousands of years after the injectors were deactivated when the Earth has long since reclaimed other Gem construction sites.