There’s nothing about our neural architecture that has “3D” built into the information it can process.

I think we are very much hardwired to innately understand 3d space in an intuitive level.

Is that just based off of something more concrete than what feels right to you? If a neural network on a computer can interact with four dimensional data, why wouldn’t we be able to?

It isn’t as automatic in three dimensions as you make it sound. Based off of the amount of learning and experimentation we do as infants, it seems reasonable to theorize that if a human were to be born in a fourth dimensional realm and to be implanted with some sort of sensory organ(s) that function in the fourth dimension, they would be able to gain an intuitive understanding of that world in the same way that they gain intuitive understandings of this one.