21、Houseki no Kuni (I don't know whether there's an English name and no idea how the proper nouns, so it's better to check the original works' wiki or something) AU from a long time ago
This one is also quite old, but I'm archiving it anyway.
In short, there is no Kongō Sensei here. The role of the teacher is filled by the god of this world, XD. However, XD is a pure hedonist; after deciding that Earth was no longer interesting, He handed over the duty of leading the remaining Gems to Dream, a Gem He created by hand (all other Gems are naturally occurring). Dream has been leading everyone diligently ever since, though he doesn't quite remember exactly when he became the Speaker.
Dream is Jade, and Techno is Pink Diamond. Although Techno has high hardness and immense combat power, he has a congenital defect (similar to Padparadscha in the original manga). He occasionally loses consciousness without warning, and the intervals between these episodes are becoming shorter. Because his condition improves slightly during the winter, he is in charge of the Winter Patrol.
One year, Techno's partner Philza (Emerald) was still adapting to the loss of an arm, so Dream volunteered to take his place and partner with Techno for the winter patrol. Dream and Techno sparred frequently; while others thought they had a poor relationship, they actually held a deep mutual respect for one another. Because Techno had conducted winter patrols for years, he was accustomed to the whispers of the floe ice, but it was Dream's first time hearing these voices (and as a fellow creation of XD, he was more susceptible to their influence). While Dream was distracted, the Lunarians attacked. Techno was taken to the moon while protecting Dream, and a portion of Dream was taken as well.
When the others woke up in the spring and heard that Techno had been taken, they were shocked. Philza said nothing, but his resentment was palpable. Tommy (Yellow Diamond), who had always viewed Techno as his most respected elder brother, couldn't sit still and immediately began blaming Dream for everything. Wilbur (Smoky Quartz), who loved stirring up trouble, joined the fray; he dug up records left behind by human civilization and began loudly preaching independence. Soon, the gems went their separate ways, each establishing their own factions.
When gems lose parts of their bodies, they lose parts of their memories along with them. Dream happened to lose his sense of love and responsibility for his companions (aka, c! Dream). After filling the missing parts of his face with the few remaining shards of Techno—regardless of whether they fit, he just wanted to piece them together—all that remained was his obsession with Techno. Consequently, he drifted away from his original friends (Sapnap the Fire Agate and George the Aquamarine). Finally, with Punz's help, he feigned a defection to the Lunarians, letting Punz shatter him so the Lunarians could take advantage of his vulnerability and carry him to the moon.
As soon as Dream landed on the moon, he went on a killing spree, fighting his way all the way to the central building. At that moment, XD appeared to stop him, saying he could take Dream to see Techno. The moment Dream saw XD, he remembered his own origins, but he brushed aside all the complexities, wanting only to see Techno. Techno had indeed not been ground into powder; in fact, the Lunarians had even cured his innate defects. Techno was shocked to see Dream, and even more stunned when Dream lunged for a hug, ignoring the risk of shattering upon impact. Techno asked Dream why he was there, and Dream replied he had come to find him. When Techno asked about the others, Dream said they were no longer his concern. XD then chimed in, suggesting Dream could stay on the moon and live with Techno, provided he led the Lunarians to Earth to shatter more gems and bring them back. Dream agreed without hesitation, but Techno refused. Dream then told him to return to Earth first: "If you still want to stay there after seeing the state of things, I won't stop you."
Techno's return to Earth naturally startled everyone, and they scrambled to recruit him into their respective factions. Techno found it utterly absurd; the Gemstones were already few in number and had to stand united to fight the Lunarians, yet even then, they frequently lost companions. Now, they were actually engaged in internal power struggles—what on earth were they doing? Furthermore, no one except Philza offered him an explanation of the actual situation; everyone's first priority was simply to win him over. Techno finally understood why Dream had defected to the Lunarians. After persuading several other Gemstones who also found the status quo intolerable (The Syndicate), he departed for the Moon under Dream's welcome.
I don't know what happens next, but anyway, the Earth Gemstones are definitely in trouble.
Supplementary Notes:
■ The original world-building setting is roughly that Earth suffered six meteorite impacts, leading to the gradual destruction of human civilization. Human soul, bone, and flesh evolved into the Lunarians, the Gemstones, and the Admirabilis (slugs) of the sea, respectively.
■ In the original work, Kongō-sensei is the core figure of the Earth Gemstones. He is a prayer machine created by the humans of the previous civilization to pray for the Lunarians on the Moon, allowing them to find peace. However, at some point, Kongō stopped his prayer functions, leaving the remaining Lunarians unable to pass on. In their despair, the current Prince of the Lunarians stepped up to lead them. The reason the Lunarians hunt Gemstones is to provoke Kongō-sensei—who views the Gemstones as his own children—into resuming his prayers, and also out of sheer boredom. Gemstones taken to the Moon are ground into powder and scattered across the lunar surface, which is why the Moon appears so bright. In this AU setting, the roles of both Kongō-sensei and the Lunarian Prince are played by XD; he's just doing it for the chaos (.).
■ The consciousness of the Gemstones actually resides in microscopic organisms within them, spread throughout their entire body structure. Therefore, losing a part of their body means losing a portion of these organisms, resulting in the loss of some memories. These organisms are most active under strong light; in low-light environments like night or winter, the Gemstones become sluggish, which is why they require daily sleep and hibernation.
■ Dream's later mask was made for him by the Lunarians. It probably contains a small light bulb or something (anyway, Lunarian technology is very advanced, so it's definitely classier than a light bulb). Regardless, it can emit light 24 hours a day, so Dream is no longer weakened by nighttime environments.