Yes and no.

Khazarians weren't likely related to biblical Hebrews in any substantial way up until 1,200 years ago.

The Khazarians were just a clutch of different cultures who all spoke Turkic and all chose to embrace the Jewish Talmud and the Jewish Torah rather than die in battles between Christians and Muslims.

Since then they've bred with both Hebrews and modern Jews of various bloodlines in accordance with the Talmudic teachings of Judaism's most respected religious scholars that has shaped Jewish religion, culture and law for over 3,000 years.

Or are they just allies aligned with the same goal. Or both?

They are all Jews by every definition. All the elves share a seat at the same exclusively elf New World Order tables. They all seem to recognize each other as equals and everyone else as chattel. They may eat each other if their Great Reset is successful, but I've seen no signs of division thus far.