“Firstly, to say that the laws of logic are either immaterial or material is to create a false dichotomy. ”
It doesn’t seem to me this is the case, unless you are speculating some sort of substance that is partially immaterial and partially material. But I don’t think anyone would support the idea that the laws of logic themselves are material in any way, and thus they would have to be immaterial.
What they happen to be beyond that is an entirely different question. It’d be like asking “what category of immaterial are they?” or “what is immaterial?”