Godel then latches onto that to create an alphabet of the symbols which then are mapped to numbers; thus formulas are even bigger numbers, and derivations are even bigger bigger numbers. So for any statements there should be a derivation that prove the statement is true or a derivation that proves the statement is false. Of course most statements will be false, but even then there will be a derivation showing so.
Then Godel does some clever manipulation to show that there will be some statements for which there can be no such derivation in either way. But that does not need the physics theory to express things about itself. It only requires to be mathematically complex enough (it'd be weird if a theory of everything was simpler than Robinson Arithmetic) and that it has rules of derivation of its statements (ie, that mechanical math can be applied to deduce the truth of the matter from the first principles of the theory).
Of course, the actual undecidable godel number and the associated physical proposition would be immensely complex. But that is only cause nobody has tried to improve on Godel's methodology of assigning numbers to propositions. He used what was simpler, prime factorization, cause it was easy to reason about, but results in astronomical numbers. But there is no reason a better, less explosive way of encoding propositions could be found that made an undecidible Godel number to be translated into something comprehensible.
But this is largely unnecessary; Godel proof forces the mathematical system to speak about itself and then abuses this reflection to create a contradiction. It means the system is not complete, that there are statements in the system that cannot be proven from its first principles and derivation rules; the fact that the one Godel showed to exist is self referential does not mean all the undecidable propositions _are_ self referential. There well could be other, non self referential undecidable propositions, that could very well have a comprehensible physical interpretation.
And, regardless of the universe being a simulation or not, the physical theory will ultimately need to deal with this incompleteness.