I define leftism as socialist, or those philosophies derived from or based on it.
I certainly agree that Jews moved left as a reaction to antisemitism. I think this happened in Europe, well before the great immigration here of c. 100 years ago. I also think that "conservative" antisemitism has been responsible for keeping American Jews on the left up through WWII. Perhaps the current persistent leftist antisemitism and leftist anti Israel attitude will change this. Not so much the Orthodox Jews, I think.
As far as I know, not being much of a scholar, or very religious, you are right that traditional Jewish teaching, in the sense to which you have referred, has nothing to do with leftism, as it far predates it. I hadn't meant to say that leftism was part of Judaism, merely that European and American (and probably European?) Jews of the last 120 or so years have more often than not adopted leftist political beliefs.
Meaning that they have not been so leftist.
You define Leftist as Socialism, others define it an being pro choice or having a sympathy for certain gun laws or other issues.
Define Socialist.
If Left is labor unions and such, it's true, and was from necessity, not any sort of Jewish tradition. It is how Jews raised themselves into the mainstream. The environs of the Right were closed to Jews.
But Jews, the People who invented the concept of Freedom escaping from bondage in Egypt, may be the least intrinsically economic socialists and greatest entrepreneurs.