Before I begin this one, let me apologize in advance if it does not format properly.
The Khazars were NOT Karaites. Here’s another one of those little “mysteries” I can help out on.
In the 8th century, as a result of the influx and influence of the Jews migrating throughout the region, the nation of Khazar, much of its royalty and aristrocracy converted to Judaism.
The conversion was performed by Rabbi Yitzak HaSangari. The result was a more tolerant and harmonious society. The Jews, who were educated in many other nations, brought with them the culture, arts, and technologies of the civilization/nations they fled from.. The direct result was that the Khazars became an Asian steppe tribal society that successfully made the transition to an urbanite society.
Eventually, the Khazars and the Balkins were conquered by Sviatoslav of Kiev. However, most of the families of the original migrating Jews remained in the region. World Wars 1 & 2, along with the rebirth of the State of Israel, led to mass Jewish immigration out of the region.
Many people, generally Anti-Semites, try to state that these people were not of Jewish blood. But this is incorrect. Genetic testing shows that they are indeed, without question of the same Jewish people who were still living in the Middle East and other areas. So, any discussion of Ashkenazi Jews not being “original” Jews is simply moot.
The Karaites were not part of the Khazars. Most of them remained in the Middle East. Many lived in Egypt.
The ruling elite may have converted to Judaism, not the entire realm which remained with multiple religions.