Genuine question, is criticism of the Israeli government, even based on falsehoods or misunderstandings, antisemitism?

It isn’t inherently but it definitely can be. It’s absolutely possible to criticize Israel’s government in an antisemitic way. In the same way, you can look at anti-Japanese posters from WWII that have racist charicatures and recognize and criticize the racist element, while acknowledging that Imperial Japan was absolutely vile.