I’ll add that using the word ‘Ashkenazim’ for Northern and Eastern European Jews and ‘Sephardim’ for Jews from Spain is separate from the idea that the Ashkenazim aren’t really descendants of persons from Israel. Ordinarily they are just considered two different groups who have ancestral connections with Israel (and that’s what I was agreeing to, not to theories about the Khazars).
Understood. There are some differences in traditions of worship between Ashkenazi and Sephardic Jews, but neither one is more or less Jewish than the other.