I agree with you partially about zog, as it's an embellishment of the truth (that being that zionists excercise significant influence in US politics, but not a total occupation), but zio is just short for zionist. Using zio as a pejorative is no different from something like MAGAt. Sure, nazis use it as a pejorative against Jews, but it has a more narrow meaning. Nazis who use zio as a pejorative are engaging in the conflation of zionism and judaism, which you are aiding in when you accept the nazi premise that zio is a pejorative for jews, and which Israel benefits from as it enables them to weaponize antisemitism against critics of genocide.