Set theory and logic are too interdependent to venture far in one whilst steering clear of the other. For instance, you'll only really skim the surface of model theory without a basic understanding of infinite cardinals.
They can indeed be used together and are interdépendant in practice at "high level mathematics"
But set theory is made of a lower level primitive (first order logic) itself being an extension of zeroth order logic.
I was saying that in the context of learning the foundation of mathematics where set theory is not the first place to begin.