i wanted to see duel, but unfortunately nothing happened
That feels like a misread. In this chapter, she literally stared Izumi down like she was about to whoop his ass for standing up for Koharu. I don't think this is romantic jealousy. I think she just hates KoharuMy guess is that Hozue's whole stick is probably gonna be she's jealous of Koharu's relationship with Izumi. I would also guess that she humiliated Koharu in middle school that made her want to stop going in some harebrained scheme of trying to get closer with Izumi.
I get that this whole manga is about helping kids overcoming whatever issues they had and becoming better people, but fuck her. I hope Izumi straight out rejects her in public and lets her feel the same humilation Koharu did. I hope the school finds out she was a bully and ostracized her.