I'll respond to only the Nature study you quoted from. The article is studying the relationship between Jewish populations, not comparing Jewish populations to Khazarian populations. You give this quote:

"With notable exceptions, most Jewish populations cluster genetically with other Jewish populations, indicating genetic similarity that often exceeds that with non-Jewish historical neighbors."

All of this is consistent with the article I linked to, which somehow reaches a totally different conclusion from the one you came to. Your quote only says that most of the Jewish populations (which mostly do not have a connection to the Middle East) have similarity to each other, which is exactly what we should expect because it was known to many available historical sources that they largely descended from Khazaria.

I personally don't think it matters whether they are Ukrainian Nazis or Khazarian Nazis in Ukraine. We already know they are Nazis. They are descended from Khazarians and in that tattoo video I saw earlier the guy supposedly had a tattoo of Khagan Bulan. I'm starting to think maybe there is an actual Khazarian conspiracy (which doesn't imply a Jewish conspiracy, though constant attempts by the ADL and Jews to censor anyone from talking about Khazarian ancestry is definitely not helping their case)? Maybe you can watch that video and weigh in?