I think part of it is the current situation lends itself to more pro-gaza headlines.
For starters the situation is evolving more on that front. Every new action is a potential headline for palestine. On the other hand Israel's position is much more static: They want to prevent the slaughter on oct 7 from happening again, and are using force to do so. That hasn't changed. You can't make new headlines out of it.
Its probably also inherent to the fact that Israel is currently on the offensive, outside of its territory in an asymetrical urban conflict. The optics on that are always going to be bad for the state in Israel's position regardless of how justified it is. Urban conflict is always a bloody mess, same with asymetric conflicts.
When israel bombs a hospital that makes a great headline. Its easy to understand and verify - hospital used to be there, now it is not. Its emotional - everyone knows in normal circumstances hospitals are supposed to be off limits. The Israeli side is hard to fit into a headline - hospital bombed after it became a military target due to use by militants, in accordance with international law and the principles of porportionality and distinction. For starters that is a mouthful to be a headline. It lacks emotional punch because now we are talking about legalese not deaths of innocets. Its hard to understand - most non experts do not know what the doctrine of porportionality& distinction is. Even if they do, we do not know in the fog of war what israel knew when targeting it and if it was reasonable at the time. Even if we did, where precisely the line is can be controversially grey. Its not like there is a huge amount of case law on this. Determing if it was legal would probably require hundreds of pages of legal argumentation. Even then, there is a whole other question of if the line international law draws is the correct one morally, which you could write a book on. Its just very hard to put all that in a news article.
So i don't think it is HN's fault that most of these articles lean more anti-israel. Its just much easier to write about things from that perspective. It is much more black and white and requires much less nuance and context.