Officially, the US has more jews than Israel, but it isn't a literal jewish state. Jews exist outside of Israel, and plenty are opposed to it. Fundamentally, no government can truly represent a full diaspora. Israel asserting otherwise is simply a lie, as all others were.

That being said, Israel can still (in the future) be governed by Jewish Law, and then it will at least be correct that it is a Jewish Religious State. But that wouldn't still represent all jews, so they still can't be used interchangeably.

This doesn't say anything about the ethnic minorities in Israel that are represented by the state as well.

All Israel can ever truly do is claim to represent Israelis. It can't ever actually claim to represent jews.