Ashkenazi Jews have a distinct genetic lineage that is a mixture of European and Levant. They are definitely, in significant part, descended from people who lived in that region. That part of their heritage (at least half, in genetic terms) left the area during late years of the western Roman Empire, and it seems to be they mostly ended up in Spain and migrated east across Europe. These were mostly expulsions, not willing migrations. They picked up a lot of European DNA along the way, but always remained distinct.

The Jews who stayed in Palestine are the ancestors of today's Palestinians of all religious groups.

Does that make Ashkenazi Jews indigenous to the Levant? Maybe, by a less standard definition of the term that prioritizes ancient ancestry over continuous occupation. Palestinians are obviously indigenous to the area by any metric, being the direct descendants of the area's ancient Jews and related Canaanite groups. Ashkenazi Jews and Palestinians are closely related populations, but that does nothing to absolve settlers of their crimes.