Universe Hopping Quirk Midoriya
Midoriya was born with a quirk, but nobody really believed him. Also, trans Midoriya (AFAB) and UA Traitor/Forced Villain Midoriya. Midoriya's original quirk is that he can teleport to different universes, but he cannot leave said universe until he dies. Time moves differently in each universe compared to his own, so even if he's lived an entire lifetime in another universe, it may have only been an hour or so in his universe. The first time he did it was when he was six, and he was still biologically female- he became Gilda from The Promised Neverland. He lived an entire life as Gilda, but when he went back to his universe he was still only six years old and it had just been two hours. Nobody would believe him, because nothing about him had seemingly changed (he had straight hair like Inko's). After TPN, there were a couple more worlds he visited, but nothing really relevant to the story.
He came out as trans to his mom, and she was supportive. They were at the store together one day when Midoriya was eleven, and a villain attacked. The villain was one of All For One's minions. Inko died, and in desperation to escape, an injured Midoriya used his quirk. Unfortunately, his body got destroyed this time, and he became a wind spirit in the world of genshin impact. A wind spirit who eventually became the Anemo Archon Barbatos or the bard Venti. That was the universe that Midoriya loved the most, and the one that turned him into an alcoholic. When he came back, his appearance had changed somewhat- his original body had technically been destroyed, but he still looked similar to his normal self, just with aqua tips in his hair and green to aqua gradient eyes, kind of similar to Venti's. Also, he had become biologically male. It had been a year in his world this time, and he appeared right in the middle of a store. Unfortunately for him, All For One had taken notice of him, and had discovered what his quirk was and could do. He was intrigued, so obviously he kidnapped Midoriya practically the second he set foot outside the store.
All For One decided that Midoriya could be a good asset to Shigaraki and the League, so he started some brutal training and gave Midoriya a few more quirks. Midoriya got a powerful elemental quirk, where he could harness each of the four elements as long as something of the element is there to manipulate. He also got a quirk where he could change his appearance at will (only able to change what's already there, like hair, and cannot do something like make himself grow wings).
While fighting a small time villain group that had been annoying Shigaraki for some reason or another, one of the villains hit him with their quirk and Midoriya, not knowing what the quirk would do to him, panicked and accidentally activated his quirk. The quirk actually just changes the colors of things, and it only turned his hair purple.
He was transported into the world of Danganronpa, and became Kokichi Ouma. He actually was in that world for a couple of years before the killing game, and he established D.I.C.E., a group of homeless kids doing harmless pranks and graffiti and things. This life left him with the most unanswered questions, but he cannot go back to the same universe twice, and even if he could there would be no guarantee that there would be anyone still alive to answer his questions.
When he came back from that life, it had only been like twenty minutes, and he looked the same aside from some new purple streaks in his hair.
Of course, there were other lives too, where he transported worlds in an attempt to get away from All For One or some other villain of hero. These worlds just don't matter very much to the story.
Midoriya was sent to UA as the traitor, and because he is a well known villain he used his appearance-changing quirk for a disguise. He made himself taller (definitely not because he was tired of being teased about being short) and took inspiration from people he'd cared about in different universes to create the rest. For his eye color, he used Emma from TPN's eye color. He used Saihara's hair from DRV3 for his hair color, and went back to Venti/The Nameless Bard's hairstyle (Genshin Impact).
At UA, he acts very haughty, and acts very discriminating against people with weak/villainous quirks and quirkless people. He uses his elemental quirk at UA. He did not intend to become friends with anyone, and a lot of people hate him. However, Todoroki noticed a lot of things that the others didn't, and confronted him at the sports festival.
They became friends after, secretly for their safety, and then they become more than friends. Todoroki knows that Midoriya is the traitor, and is keeping his secret. Midoriya tells Todoroki stories from his lives in other worlds all the time.
The war arc doesn't happen, but Dabi does reveal himself.
Todoroki already knows because Midoriya told him, and this raises suspicions among the league that Midoriya is betraying them. To test this theory, the next time the league attacks, Dabi goes to kill Todoroki, and Midoriya interferes, proving their theory correct. The league then outs Midoriya as the UA traitor and attempts to kill him, only for Todoroki to return the favor and save Midoriya.
Tsukauchi interviews them along with all of the class, both Midoriya and Todoroki get some therapy, Todoroki is removed from Endeavor's care, and Erasermic adopts Midoriya.