This is false. Godels incompleteness theorems only prove that there will be things that are unprovable in that body of models.

Good news, Newtons flaming laser sword says that if something can’t be proven, it isn’t worth thinking about.

Imagine I said, “we live in a simulation but it is so perfect that we’ll never be able to find evidence of it”

Can you prove my statement? No.

In fact no matter what proof you try to use I can just claim it is part of the simulation. All models will be incomplete because I can always say you can’t prove me wrong. But, because there is never any evidence, the fact we live in a simulation must never be relevant/required for the explanation of things going on inside our models.

Are models are “incomplete” already, but it doesn’t matter and it won’t because anything that has an effect can be measured/catalogued and addded to a model, and anything that doesn’t have an effect doesn’t matter.

TL;DR: Science as a body of models will never be able to prove/disprove every possible statement/hypothesis, but that does not mean it can’t prove/disprove every hypothesis/statement that actually matters.