That's not what happened with Shura. She only questioned him about what he was doing and about his eye, while he kept completely silent.
I think that's also because Shura is much better at dealing with people, especially with Yukio (happened several times). While Rin/Shiemi/Bon each has their flaw on communication (also happened several times)
I'm surprised that Shiemi didn't blush at that moment or gave us any sign such as her mental though: "OMG he's hugging me, he's hugging me, what should I do now?!" But no, she did exactly what a good friend would do, giving him her moral support.
Shiemi never knows that behavior is also a sign of possible love interest since it seems like she isn't even aware Yukio likes her. She probably thinks it means Yukio is in serious trouble.
And I don't really count her response as some support (as chino already explained earlier), although she said that because she is concerned about Yukio
She failed at supporting him, but she at least tried. The things she said and did before turning the conversation around were all great support. She only botched the final.
Yes I meant the final ones. Before that, she was like how she has succeeded two years ago.
After reviewing chapter 93 I just realized, she probably isn't quite sure whether Yukio felt better after the conversation two years ago. So she thinks she might fail last time, but not this time. Unfortunately it's actually the opposite.
it seems weird to say there is any "competition" or "love triangle" when only one of the three (I mean Rin) was actively pursuing love interest
Rin thought Shiemi liked Yukio, while Yukio thought Shiemi liked Rin. Even if they were wrong, they both thought the other had what they wanted, that's what makes people compete with each other.
Plus, regardless whether they are actively pursuing or not or whether they are aware of the others feelings or not, the fact remains that both Rin and Yukio love Shiemi, which inevitably makes this a love triangle.
Maybe it's a love triangle, but I wouldn't call it a competition because if you are competing, I suppose it means you work hard for it. But neither of them works hard to pursue love.
On the outside, he seems 'okay', but... I'm sure if Yukio doesnt want to be that close to her, having her around because of Rin keeping her close doesn't help.
Yukio is jealous of Rin. When he spoke with Toudou near the end of the Kyoto arc, there was that scene where he was remembering all the things Rin was or had that he thought where better than what he was or had, and he was wondering why he can't be like that or have those things. That's what I would call jealousy. And there's also that time at the end of the Giant Whale arc (or was it somewhere else?) when Rin said he's going to surpass Yukio, and Yukio thinks "that's my line". There are plenty of other example, but to me it's clear Yukio wants to become a better person, and he wishes he was the kind of person who can be a good brother, a good friend, a good love partner or husband, but he doesn't think he can, at least right now.
OK, that's a little complicated. When I say "he was not jealous" I just mean the Shiemi part, not including other parts. Yukio does envy Rin's personality (what you described as "a better person"), so he thinks he also wishes to surpass Rin. Even though Shiemi is included in those flashback as Kannra21 quoted, the major part was
the little dog Shiro. I would say Yukio started to think about it long before he knew Shiemi. And although Yukio's complex thoughts about Rin was first revealed at IK arc, at that time we aren't even sure whether he loves Shiemi. My point is, "Yukio envies Rin's personality" and "Yukio cut off the possibility to have romantic with Shiemi" aren't really the same thing. If Shiemi doesn't exist, Yukio will still envy Rin for other events. If Rin doesn't exist, Yukio will still hesitate to start any relationship because he hates himself.
However, things changed a little in chapter 93. IMO it's the first time we see Yukio envying Rin's relationship with Shiemi. Though I think that's mostly subconscious. Consciously he thinks he's OK or even kind of push Rin and Shiemi together.
(I will add I can not see the links in the original post from Kato and Mephisto, all those older links are broken now, or my phone hates Manga fox ).
Mangafox is weird these days, so that's why I changed the links to mangapanda