We should note, on this topic, that Job mentions “priests” at least once and I think more than once. Since Job was a man of God, what kind of “priests” was he thinking of, if not of Aaron?
Lending credence to Job being a real and historical person, we have Ezekiel 14:14, where God says, “even if these three men–Noah, Daniel and Job–were in it, they could save only themselves by their righteousness, declares the Sovereign LORD.”
My Biblical commentary (New American) says Job was not a Jew, but I reject much of my Bible’s commentary as faithless (discounts miracles, etc) or inaccurate anyway.
I’m aware of Bl. Anne Catherine Emmerich’s statements (not approved by popes) about Job being Abraham’s ancestor, but I find a lot of her statements contradict those of St. Mary of Agreda in her “Mystical City of God” (Life of Mary) which has been approved by several popes. So, I’m skeptical of Emmerich’s comments.