Kinda different from the Ln where azusa doesn't seem to show any remorse
WN, or LN ?
In LN, she did feel bad about it, but when she realized it, it's already too awkward to start talking to her brother again. Saying sorry is not easy.
Also remember, she's in love with Ryouma and she really wants to win his heart. Unlike romcom male protagonist who are typically passive, the heroines are not just going to sit and wait for god to trigger an "event" to increase affection point, they actively try to show their affection.
Back to Kotaro and Azusa, they're caught in a deadlock. They need a trigger to push their back, so they can restart their interaction.
Shiho became that unexpected factor, and bridged both of them to start talking again.
And while the trigger for her to start getting interested to Ryouma is his similarity to her dead brother, she did want to love him as he is (not just replacement). It doesn't end happily for her.
The way the dude acts. He not only seems to have a harem after him like a harem protagonist, but the way he reacted to the FMC interacting to the MC was not just creepy, but he acted like he believed himself to be a harem protagonist.
Unlike isekai harem protagonist who at least know how it felt to be unpopular in their past life (thus they either distrusting the girls' affection, or enjoy the harem life), Ryouma never know any other kind of life.
It's always people naturally liking him, so he's just a privileged prick with twistedly narrow world view.
But he doesn't believe he's harem protagonist, he doesn't see the world as a romcom story so it's an alien concept.
Also for the novel readers, is it the same set up ?
Kotaro's mother married again with Azusa's father? Rather than she's actually his cousin? My memory is really blurry on this part and can't find the passage back in the book.