Katsuki offers a job at his agency. Izuku says, “no, thanks, I have a job that I really like”, and Kirishima, because he's Katuski's bro-est friend to the end, has to tease Katuski about getting rejected.

And Katsuki, realizing that his intentions might not have been clear, explains what he meant specifically for Izuku. He says that if someone is important to you, you should make sure they know. AKA he’s explicitly telling Izuku that he wants him to know that he's important to Katsuki. And then, and then, adds that Izuku should do things for himself, that he should be doing whatever makes him happy. And this line in particular is so sweet, because it’s such a lovely encapsulation of how much Katsuki’s grown up. He’s saying, hey, man, we aren’t kids anymore. You didn’t bruise my ego, I’m not pissed off, I just want you to be happy. If teaching is what you find fulfilling, I’ll support it.

In context, Katsuki effectively spends the whole car ride telling Izuku that he doesn’t want to work with anyone but him (“if any interns had come along saying they want to surpass me…”). He's saying that nothing has changed, he hasn’t moved on, he still actively wants Izuku by his side. He’s letting Izuku know that there will always be a place for him at Katsuki’s agency if he ever changes his mind, but that he wants Izuku to be happy and is glad he’s found something (teaching) that makes him feel that way. There isn’t anger. Maybe some disappointment, but not because I think he’s feeling totally rejected by Izuku. He's actually just giving him affirmation after affirmation that he still cares about Izuku, a lot.

And yeah, because most of Horikoshi’s dialogue has double meanings, Katsuki can definitely be read as a (somewhat inadvertant) wingman for Izuku and Ochako, but honestly, those two instances are fairly separate. The conversation in the car is all about him and Izuku, and if Izuku takes that to heart and goes to Ochako, I don’t see that as dismissive of Katsuki. I see that as a testament to their friendship that, for the first time in his life, Izuku actually listens to someone else’s advice and does something for himself lololol.

Deku tried. He's trying. And he wants to do better in the future, and is actively looking for ways to do so. Because at the core of him, above all else: Deku is the name of a hero.