You can answer the question of Ashkenazi Jews (the primary driving force of Zionism and colonialism) being from the Levant by using modern samples. You see there are the actual people of the Levant and they never left. If your Ashkenazi Jews were from the Levant then they would overlap with the Levantine people in DNA in at least some quantity. They do not overlap. Their DNA overlaps with Germans, Ukrainians, Russians, etc. because that’s who they are.
Even if you “mix” it doesn’t change your heritage. You always pass down the heritage form descendant to descendant.