
Tbh just like some comments here, at first I thought it will be something like grooming, but when I tried to re-think about the relationship they have, I changed my mind.
The older guy taking care of the younger guy because he wants to escape from his guilt/sin towards his deceased younger sister. Especially whenever he find out that the younger guy was bullied by his schoolmates, that feeling is getting stronger due to the same experience his sister had.
"If I save this guy, it'll be my atonement towards my sister".
Currently, the older/younger guy has no romantic feelings towards each other. Their relationship is still quite fragile. The older guy wants to atone his sins towards his sister, the younger guy wants to live normally with his mother.
Both of them have a goal for their own satisfaction. The younger guy still doesn't 100% trust the older guy. If there's a problem that will attack the younger guy, I'm afraid it'll destroy everything.
Maybe it'll take time for the relationship to be changed, but I'm not certain about it since I don't read the novel.

So Kyungbin and Mi-rye will really have no contact (or more like Mi-rye tried his best not to be seen by Kyungbin) for several chapters.
I don't understand Korean, but from the raws with Google Lens' help, I think it indeed has strong connection to Yugun.
CMIIW, we all know Yugun has a weak body since young, but he's actually much weaker before just like what he said. It's to the point their parents couldn't give full attention to Kyungbin, and he understood the situatiin (though he might be feel lonely). Also, Kyungbin has been sensitive towards Yugun's condition since they were young, since he's the first one to realize that Yugun's in fever... I guess? seeing his lil bro's face color.
One day, Kyungbin had an important competition and seems like his family wanted to watch him. Their mother called Yugun for something but Yugun answered while hiding his face in the blanket------ turned out he got another attack, to the point their parents had to rush him to the hospital and made Yugun wear the oxygen mask.
Yugun saw Kyungbin (idk if Kyungbin has finished the competition or not), he cried in pain and said "I'm sorry..." to Kyungbin, most likely feeling really guilty and sad because he actually tried to hide the fact he's in pain in his brother's important day.
Since then, seems like Kyungbin tried his best to not make anyone in his family get worried by anything (since Yugun's condition always made their parents worried), until the bullying case was reported to the teachers. Kyungbin tried to stay quiet about his senior's behavior, but since Mi-Rye reported it to the teacher, of course it will be reported to Kyungbin's parents. His mother came to the school crying, and Kyungbin felt really angry to whoever reported it because he didn't want to see his parents getting worried again.
But don't worry, Mi-Rye and Kyungbin will make up after the competition! Though I forgot to translate what they said to each other...
Lmaoooo he is the exact copy of his mother (face, temper, brain)