This is my pitch of concept idea for Krypton movie (if there's any) with some of my own twists and versions.
Setting and Characters: It's evolved around the story taking place in New Krypton before the destruction. The characters consist of Jor-El, Lara Lor-Van (Superman's mom), Brainiac, General Zod, Zor-El and Alura In-Ze (Supergirl's parents) and Kara Zor El as well as Tomar-Re, Green Lantern cop responsible taking care of Krypton.
Concept Ideas: 1) It start with Jor El on a trial witness by everyone on New Krypton (like the scene of Hari Seldom from Foundation series) on base of accusing Brainiac as a fraud and a liar. Jor El shows evidence of ancient books made by ancient Kryptonian he found stating that Kryptonian have the abilities to fly, superspeed and super strength, laser beam, cold breath etc but somehow lost their abilities for unknown reasons that can only be explain by Brainiac. Brainiac is immortal being from planet Colu fallen from the sky way back in Ancient Krypton and seen as an angel by Kryptonian where their civilization thrived with his modern technology with his guidance and all sources of history and knowledge cited by him instead of Kryptonian keeping it themselves. But the case against Brainiac has been dismissed for Brainiac side by the Krypton Councilmen.
2) There's also idea General Zod and Jor El would create a coup d'etat against the Krypton Councilmen and Brainiac only to be defeat and broken by Tomar-Re, Green Lantern assigned to protect Krypton. Jor El and Zod would have imprisoned as treason in prison facility lighted with Green Kryptonite. At one point, they break out and head to Ancient Krypton where they would discover their ancient powers after being hit with yellow sun on that planet. They also find that millennium ago via drawing and sculpture on the wall, Brainiac landed on this planet from planet Colu, kidnapped one of the Kryptonian to be an experiment thus creating Doomsday. This explain why the planet is unhabitable in the first place and why Kryptonian left the planet to live in New Krypton at expense of their power since New Krypton only has red sun. Over the years, Brainiac makes himself some kind of angel to Kryptonian since they had to adapt to new environment and has changed some history event to teach the new generation. All powerful Kryptonian in the past becomes fiction and myth.
3) Another idea is the existence of Kryptonite in New Krypton. Green Kryptonite is used as weapon like laser gun that shoots green beam that able to kill Kryptonian and also place in every lightbulb in Krypton as security measures implement by Brainiac centuries ago. Kryptonian wears Gold Kryptonite as jewelry and accessories for fashion without any knowledge that Gold Kryptonite absorbing sun from giving Kryptonian powers. Brainiac also has Pink Kryptonite all over his robes as accessories which have power to pursue anyone into his own will (Jor El also known and did went to trial to show everyone about this discovery only to be reject and debunk.) Red Kryptonite would be used by Brainiac to create Doomsday and also human experiment since Red Kryptonite are unstable for causing bizarre physical mutations.
4) Tomar-Re would have bigger roles as protector of Krypton. He would have working under Krypton government, saving people just like Superman on Earth and beats Jor El and General Zod's coup d'etat before fights against Brainiac and his cyborg. He would be the one using all his will power to protect the Krypton core with his Green Lantern ring all by himself to stabilize the planet before died. Brainiac sees him as competitor for the love of Kryptonian and harbours jealousy.
5) After almost losing love of people from Krypton, Brainiac uses pregnant Lara Lor-Van to take all his accusations to Brainiac and points it all to General Zod and his followers. In the end, Jor El makes a deal with Brainiac to leave the planet in exile with his family in exchange for his silence but when second coup d'etat happens, Brainiac only creates a small pod enough for a baby, Kal El. I like the twist that the rest Jor El only creates ship small enough for a baby is because he never did create it and it was all Brainiac as some kind of sick revenge. And I find it interesting that instead of classic story where Jor El warns the people of Krypton that their planet is dying, Jor El tries to expose Brainiac as a fraud which his action lead to the actual destruction of Krypton which if he just let go, the planet would still live but under the utopia lies by Brainiac. Anyway, Jor El keeps his memory as hologram and redirects the ship to Earth.
6) General Zod was betrayed by Jor El, sent to a special facility where criminals in Krypton will be exposed with Black Kryptonite which separate good and evil side. And somehow a fight happened between Zods and the authority which the good side of General Zod died leaving the evil version left to lead the army for a second coup d'etat. General Zod would have leftover of power he got from Ancient Krypton's yellow sun and proves to everyone Brainiac has lied to them by flying and laser his way to Brainiac in city of Kandor.
7) Brainiac finally snaps during General Zod's coup d'etat, decides Kryptonian are no longer matters, gets into his skull shaped ship and shoots beam straight to Krypton core after he shrinks city of Kandor and it's people as souvenir to memorialize. I honestly don't know where to put Zor-El and Alura In-Ze, Supergirl's parents into the story but according to comics, they would help Kara Zor El into the ship and perhaps somehow Kara would have her dog, Krypto and her horse, Comet that can fly. I don't know. Maybe Kara was somewhere far while the planet getting destroy and her parents did the same deal so she just racing to the pod with her horse and dog but when she arrives, her parents' pod destroy in all carnage and they just put her in the remaining pod. So anyway, General Zod loses all his powers and all his soldiers and himself are imprisoned into Phantom Zone by Brainiac.