Well how is it relevant then? Im happy to be corrected but I dont see how its relevant to this post

It just tells you that there is a well approximating NN for any given function. It doesn't tell you how to find such a NN and it doesnt tell you about extrapolation capabilities of a NN which is well approximating on just a subdomain (which is what this post here is mainly about) either.

The universal approximation theorem in practice just gives a justification for why using NNs as function approximators could be a reasonable thing to do. That's already pretty much the extent of their relevancy to practical issues though