This isn't Reiya's fault, or Reiya's problem, and he's not some bad person in Youta's life who's caused him unending grief
While Reiya isn't at fault for Youta's grief, he is very much the cause of it, indirectly
or directly, though not to imply Reiya owes it to Youta to alleviate his grief. I am not calling him "malicious", I am calling him "clueless", malicious is how Rei would come out if one starts interpreting him approaching Houjou as an act of "therapy" for Youta.
when nothing between the two of them is actually hostile or even broken.
Even if Youta understands that his brother isn't at fault, there is some resentment coming from Youta, he did want ot desperately beat him at something after all, and this resentment only subdued thanks to Houjou's involvement, though not necessarily fully disappeared, so I wouldn't call their relatinship entirely intact either. And even if there was no resentment altogether, there are still boundaries of how much one should be getting involved with someone else's personal life, and it doesn't seem to me that Rei's close enough with Youta to start randomly approaching his friends who haven't been introduced to him. Or at the very least, they are not close enough for Youta's grief to be Reiya's problem, therefore I can't see how Youta's relationship with Houjou is Reiya's business.
Maybe I've missed something egregious in the plot to this point, but nothing points to Reiya being hip to the problems Youta has had with the girls at that school, and nothing points to Youta bringing his problems home to his brother.
Yeah, as I've said, clueless. The ridiculous premise of this manga, this pipeline of girls cozying up to Youta to get closer to Reiya, and the part where Reyia ends up taking everything whenever he's competing with Youta, and the grief this all ends up causing to Youta, this all flew past him.
If anything, Reiya talking with Houjou is setting up a resolution to Youta's problems, because it opens the door to everything finally being put out into the open and setting up actual pathways to communication.
Story-wise, yes, a resolution is being set and communication will happen, but not because Rei is taking active and deliberate steps to help Youta's situation, but because that's how this story will play out because Rei happened to bumble into it. If Rei explicitly sought
communication about Youta's problems, I could think of a simpler approach that wouldn't need to involve making contact with Houjou first.