I've honestly been wondering about this for a long time too, but no matter how much i look at it, i just cannot seem to figure it out.
On the other side, it could be because of the realistic nature of this manga. Let's not forget that social anxiety could be called a mental illness (but i don't like to refer it at such) and it could be that he is just minding his own busniess.
Unlike Kii, Tomoki doesn't seem that focused on helping Tomoko. But the problem is that Tomoko doesn't seem to be aware that the way she is living her life isn't normal. It could be that Tomoki has always been used to seeing Tomoko being like that, and as a result doesn't seem too bothered about it?
I don't really see him as cold, but more like really naivite. Probably naive to the point that he could surpass Yuu, in all honesty. Unlike Yuu, Tomoki is aware of the way that Tomoko is living. (however, this could be arguable)
But then, it could be because of the fact that they somehow lost the strong bond they had in the past. (Which in fact again is arguable, because of the omake chap "what if i took care of my little brother", in which he said that he would prefer a shitty sister instead of the kinder one"