Even if Khazar theory was true, it would still mean jews are indigenous to the levant.
For those not familiar, Khazar theory is a largely abandoned theory that Ashkenazi Jewry is mostly made up of Khazar converts to judaism. Khazars are a multi-ethnic conglomerate of mostly Turkic peoples. Its largely abandoned as ashkenazi jews have been proven to have levantine DNA.
In judaism, when you complete conversion, you become fully jewish in every sense.
Yes, converting doesn't change your DNA. However who is considered jewish or not isn't determined by DNA.
For example, if a woman converts to judaism and has no jewish DNA, when she has a child, that child is considered jewish. In judaism, your jewishness is tracked through your lineage, which includes anyone who converted, not DNA.
It is up to jews and jews only, who is considered a jew. Only we get to define what makes a jew a jew.
The idea that only jews who have levantine dna are indigenous is a direct attack on jews determining who is and isn't jewish, as it is implying that those who convert are not jewish in every sense like judaism states they are. It is imposing a foreign system onto us.
"But clownie, doesn't that mean people could just call themselves jewish to claim indigenousness to the levant?"
No. Because to be considered jewish in every sense, you have to go through conversion. If someone who isn't jewish wakes up one day and starts calling themselves jewish without converting, they are not jewish. They are a cultural appropriating arsehole who is lying about being jewish and is not considered jewish by jewish law.
The conversion process is central to how jews determine jewishness. We have laws in Judaism for that. We have defined who is or isn't a jew.
Whilst Khazar theory is false, hypothetically speaking if it was true, they would still be indigenous to the levant since they are still jewish in every sense.