I think most of the sane public understands that Israel was aggressive in Gaza but did not deliberately target children. The reality is that you can't conduct a war in Gaza without hurting civilians because its such a densely populated place, and the lines between civilians and combatants barely exist. So either you accept it and move on, or you grant Hamas an immunity (which was pretty much the situation until October 7th). Given that, it's not clear what justice and accountability you are looking for. Are you looking to investigate each child death as a murder case? Do a Nuremberg style trials for Israeli leaders?

The world will move on, because most accept while this was bad - doing nothing was even worse.

Not really sure what to say here. Maybe it’s a lack of empathy or imagination because the victims are Palestinians?

Perhaps a good thought experiment would be to swap out Israel and Palestine with some other similar (real or fictional) conflict to help you think through your apparent confusion.