This might be kinda a long rant, but I've been overanalysing Sero and Katsuki's relationship a lot and need people to know. Ofc its a rare pair ship so not a lot of content of them interacting in canon media together, however that doesn't mean their relationship lacks nuance like most ppl make it out to be.
It's cute and silly to think of the banter and how Sero is usually just teasing Katsuki or trying to rile him up with his comments, but there's also more than that. Boiling it down to such a simple dynamic doesn't define them, and although they might not be the closest of best buddy friends I think Sero understands Katsuki A LOT.
For example in this panel where Katsuki is swamped with fans of his fight with AFO, Shinso asks Sero first and foremost why Katsuki seems uneasy. Since they've been friends for a while Sero knows that Katsuki likes attention but not to be overwhelmed by many people all at once.
Sero also manages to regulate Katsuki in multiple scenes where he points out or makes him realise that he's not acting right and needs to chill.
Sero also regulates Katsuki by reminding him to not push himself too hard. When everyone went back to UA Sero was the first and only person to question Katsuki for being present in school, obviously implying that he's worried about his health. Since Katsuki was wounded really badly this makes sense, however none of the other classmates or teachers took time to check on Katsuki or question if it's even safe for him to be out of the hospital.
And although it might seem a little one sided, with Sero mainly regulating, understanding and worrying about Katsuki, that's to be expected. Katsuki is one of the very main characters, a deuteragonist, Sero isn't a very focused character. We don't know anything about his past or origin so interpreters can't fully understand him. What we mostly know is how he's kind of a comedic relief or "gag character". That doesn't make him less nuanced or boring to analyse though, because you're given the option to have a much broader interpretation of who is, (or who he might be).
