The first mention is with the indefinite article: “a” Jewish state. The second one, crossed out, is definite, and was changed to make it into the State of Israel. Naturally the two were equated, but in the fullness of time, it will be apparent that the name “Israel” was the wiser choice, regardless of which one sounds better.
You may be right....I'm not sure. I do know that a lot of people would be less confused....Biblically, if they would have called themselves Judah! But.....Israel is fine with me as it does encompass Judah also.