Saying that Izuku doesn't care that Katsuki bullied him is wildly inaccurate. Izuku cared that Katsuki bullied him. He told Kacchan he was being mean when he was being teased. He stood up to him because he knew what Kacchan was doing was wrong when he bullied other kids. He called him an idiot for s*cide baiting him. He fought with Katsuki over and over in their first year just to make Katsuki hear him("This is why we never have real conversations!") and stop treating him like someone who was worth less just because he was Quirkless, or because of the wrong perception that he'd been looking down on Katsuki the whole time("Is that really what you thought!?"). He had to fight to get it through Katsuki's head that he wanted only to chase after him, to be his friend, because Katsuki was too thick-headed at the time to understand. ("You were someone amazing who was actually in my life!!")
It mattered to Izuku, and he didn't like it, and he called Katsuki out several times for it.
Izuku chose to forgive Katsuki for it. For all of it. Because this is a story about reaching out and offering people a hand, even when they may not deserve it.
The Vestiges said it themselves, citing Kacchan specifically as an example: Izuku is the person who will always choose the HEART that lies inside of someone and reach out.
He chose Kacchan's heart a long ass time ago. He never held a grudge on him a day in his life, only knew that Katsuki COULD be better, and he became excited as Katsuki slowly grew into that person, into his friend. ("I never thought that I could be able to have a normal-ish conversation with Kacchan....I'm too blessed!")
You can disagree with that choice, and bullying in real life is of course a different animal all together than in fiction. but it is intrinsically part of who Izuku is as a character, and how he has literally always been written. He tries to save Shigaraki, the BBEG hellbent on destroying the world, for god's sake.
It's also intrinsically part of Katsuki to have tried to make up for his past shit, and he NEVER expects Izuku to forgive or treat him any different! He literally says, "it doesn't change a thing" during his apology, but he does the fucking work anyway, including devoting himself to helping Izuku bear the burden of OFA, and risking his damn life again and again to help Izuku. And on top of all that, he leads the project and throws the most money out of his whole class into the OFA suit that is meant to give Izuku his dream back, It could even be that it was at least in part, his idea in the first place! (Obvs that speculation BUT I'm betting it was him and AllMight's idea)
And yes, he HAS done the work, not just through his actions, but through heavy introspection; if you're paying attention to him in the narrative and not just viewing him as a one note character who is angry all the time for no reason, you can see when he gets quiet and thinks.
To be real fucking honest, I wasn't even expecting him to state his apology so raw, so explicitly like that in the first place. It's a Shonen action, after all. But Horikoshi wrote it as one of the most emotional beats of the story, tied up in the deepest most intense relationships of the story.
The implicit and explicit development that Hori put into Katsuki is insane if you're listening to him instead of viewing him as nothing more than a shitty bully archetype.
Whether it's deserving of forgiveness was always up to only the character in the narrative, Izuku, to decide. BC this is fiction, and these are characters, and they serve a purpose to a theme.
And that theme was never "get revenge on your former bullies", as much as some people in this fandom want it to be.
