I think that's the point of this arc. To show that he is full aware but chooses inaction for personal ease. He clearly knows his mother is a problem yet rather than say anything he allows her to continue making her more and more insane. He is smart enough to figure out something happened with the girl he was getting interested in, yet chose to turn a blind eye again for his mother. If he was nearly as smart as he seems he would know you can't strangle yourself yet he allows that to be the end of him talking to his dad. He suspected the cupcakes and yet decided not to warn the teacher at any point. He is now only feeling guilty because it will affect him.
I think the whole arc is pointing to how inaction is just as bad as action in many cases and so he will be punished because he is at no point taking accountability. It may not be in him admitting himself as a murderer but even in stopping his mother's obsession which harmed him and those around him. The closest to redemption he will get is killing his own mother when he breaks and then going to jail for that crime and learning the horror of inaction.
Once you are in the grasps of an emotional manipulator like his mom, it's really hard to get out. They will twist and turn everything you do and say against you, they build a prison of feelings of guilt and duty. It needs a very strong motivating moment to cut those ties.
In regards to the cupcakes, there's the fear for your personal safety added, "what will my bullies do to me, if I don't hand over the cupcakes?". In a rational mode it's easy to say "nothing they do to me, will be worse what might happen to her", but that's not how a brain normally works. Much easier to fall into rationalising it as "well, she might get a bad evening, but it won't kill or long-term harm her".
There's a reason most people need therapy and/or years of inner evaluation and work to break out of it.
That said, in regards to the actual story of the Manga, I think you are right, that he's mainly there to show the consequences of inaction and of course nothing I said should shield you from repercussions, if your inaction - as understandable as it might be - does harm others.