That could not be further from the truth. Israel and the Jewish people are one and the same. Israel is founded on Jewish principles, adheres to Jewish laws, enables the Jewish people to fulfill their national destiny, and represents every Jew on earth. You cannot separate the two.
> what other country in the world can you say that a country is identical to its people?
We are unlike any other nation or state on earth - I mean, we are DEFINITELY judged differently! lol. Indeed, you cannot judge us like you would any other state, because we are unique. E.g. there is no state that is generally considered the national home of the Christians, or the Buddhists, or the Muslims.
Legally, all Jews have a say in Israel's decisions via the Law of Return, whether they use that privilege or not, so at the legal level there is a level of accountability.
> When Israel does something wrong, like kill civilians and/or foreign aid workers, do the Jewish people all over the world collectively bear the guilt of it?
Yes, they absolutely do. You are correct in your assertion that you can't have it both ways, and we aren't asking for that. All Jews worldwide should be judged on the actions of the Israeli State, because Israel is the nation-state of the Jews.
Conversely, when Israel does something good or right or praiseworthy, every Jew around the world is entitled to that praise, and feels proud of their home, even if they are currently not living there.