I'm no expert, but I can give you my perspective (Background: I'm Israeli, and consider myself fairly liberal politically).
> Honestly I'm really confused every time I try to understand Israel. Ordinary terms like citizenship, borders, immigration, and statehood are all in dispute
I'm not sure what you mean by in dispute here. Most of these are fairly well-defined when it comes to Israel. They're not even unique definitions - Sweden is the state of the Swedish ethnic group, Germany of Germans, Japan of the Japanese, etc. Israel in its conception is the land of the Jews.
There are complicating factors, which is that history you alluded to. While it certainly seems from the wiki article that the "historical Palestinian national identity" is something that is still argued about, I think the relevant part isn't so controversial.
Around the mid-19th century, the land that is now Israel (and was back then referred to as Palestine) had mostly Arab inhabitants, with a small Jewish population. Jews around the mid-19th century started a plan to go back to the lands they were removed from two thousand years prior - and many Jews started (legally) immigrating to Palestine and buying Palestinian lands. This caused there to be a fairly large Jewish population by the time 1948 came around.
Between 1900-1948, that land changed hands several times, eventually ending up under the rule of the UN, which made a plan to divide the land into a Jewish country and a Palestinian country. The Palestinians refused, and fled the land, as several Arab countries decided to attack Israel. Here there is some disagreement - were the Palestinians encouraged to flee by their leaders? Were they pushed out of Israel? Those are more disputed facts (I think for sure, some of both things happened.)
Israel won that war, effectively cementing most of modern day Israel, minus some (fairly large) territories. The Palestinians that stayed in Israel and didn't flee, became Israeli citizens. The hundreds of thousands of Palestinians that did flee became refugees in other countries.
Then the Six Day war happened. (Israelis generally consider the war to be started by others, though this is certainly disputed.) During this war, Israel took a bunch of extra territories, and with it, the Palestinian refugees. However, Israel didn't officially annex the regions or give the refugees citizenship, rather, kept them (and still to some extent keeps them) as refugees.
I think that's the majority of the story, from a (definitionally) Israeli perspectiev.