I shoulda put "knows" in scare quotes because, although she does just let off steam in her native tongue, he's put all her declarations of affection in that particular box to avoid dealing with them. His accumulated childhood traumas -- here in particular, capped off by his experience of failure and abandonment with his first love -- have left him believing he can't be loved and, even if he somehow were, he wouldn't be worthy of that love. This is why Yuki goes to such insane lengths to remind him that's not the case from the familial side and why Masha is directly spoiling him now and will soon begin openly and relentlessly pursuing him with serious intent from the romantic side, all to break that mindset.
I understand what you're trying to say, and normally you would have been right. That his childhood trauma made him do what he did. That it's the reason why he ignored the fact that Ayla often said her true feeling in Russian because she thought noone understood her (including those vents).
Unfortunately his childhood trauma and his "mistake" when he supported his sister were also stupid.
It's understandable for a kid to misunderstood the silence after his piano recital as something negative, but it's been years! Someone (his sister, parents, friends, anyone?) should have told him the truth about that silence reaction. News articles, testimonies, there should be a lot. Rather than noone telling him anything (you knew that the sister has repeatedly told MC that he's loved), it's most likely that MC has reacted similarly as he did towards Ayla's confession: denying it even though it's practically shoved onto his face. Either that or it's stupid writing.
It's a backstory filled with plotholes, and author used that "trauma" as the reason for MC's ridiculously twisted self-esteem. MC stopped supporting his sister because he felt guilty that the lowly yet capable him helped his sister win, and thus made someone (a stranger at that) lose. He regretted helping his sister because he felt sorry over a stranger. He felt that he's too lowly to make that stranger experience lost, and yet he also thought that he's so capable that he's the reason why that stranger lost.
No wonder
ActuallyArma said in his spoiler that
there's no real progress on their romance even after 7 light novel volumes.