I’m totally lost on why you would think that.

I think Gödel’s incompleteness theorem and undecidable problems show something about reality, or perhaps mathematics, rather than the human mind.

I don’t see what this has to do with the human mind, though. I would say the human mind can definitely be modelled as a computer of some sort, it is a computer, but not one that resembles a commercially available computer. They have significant differences, but I think theoretically one could write a program that would mimic the way the human mind works. It would have to use AI techniques like neural networks, and be able to rewrite itself in limited ways, which we haven’t figured out how they work. But I don’t think it would be impossible.

All it means is that the mind doesn’t operate on formal logic.

No.

Someone would probably need to have dual PhDs in math and psychology to confidently answer that…