I’ve often thought that a lot of mental anguish in young Wittgenstein’s life could’ve been prevented if Gödel’s incompleteness work had come a little earlier and he could have known how big the windmill he was tilting at really was.
Tractatus is basically the opposite of "windmill tilting", it concludes that the vast majority of philosophical "problems" end up being essentially "windmills" in the context of that expression, and that what remains is trivially solvable and not particularly interesting.
Wittgenstein, during his lifetime and after, was often confused for logical positivist, that is all that matters is logically provable statements. But it's quite clear from his further writings (and a thoughtful reading of the Tractatus) that what is being said is: if you're limiting your discussion to logical statements (i.e. philosophy has he understood it at that point) then what you can talk about is limited to logical facts and their consequences... unfortunately this doesn't cover much ground in human experience. For all of those other parts of human life, (logical) philosophy doesn't have anything to say. Hence the concluding “Whereof one cannot speak, thereof one must be silent.”
https://plato.stanford.edu/entries/wittgenstein-mathematics/...
Talking about the Tractatus, I would suggest that Godel's work would be considered "nonsense", in that it attempts to use (mathematical) language to describe language, which is an invalid operation. This opinion went very much out of fashion, I suspect because computers do these operations with great success, but I believe he is saying something deep about meaning here, not about symbolic manipulation at all. But Wittgenstein didn't publish anything after the Tractatus (except a spelling dictionary for rural Austrian schoolchildren), and what has been published posthumously is extremely difficult, so this is probably a question for a very small number of subject matter experts. So not me. I'd ve very interested in better-informed opinions.
If anything he would probably be very critical of the idea that it has profound insight into anything beyond niche questions of higher order math and computation. It makes sense in that context, but then it would be similar to the philosophers he criticized as constructing houses of cards out of "language games" if you were to apply it to something to which it has no contextual relationship at all, in which you case you could say it is "nonsense" when it outsteps the bounds of sense. Later Wittgenstein is not really concerned with fundamental, Platonic, truth. In fact, he is outright critical of the very idea. His later writings are more about method. He's far more interested in clarification as the goal of philosophy. He wants to dissolve seemingly intractable questions to reveal how they are the product of nonsensical language games filled with mistaken assumptions.
I don’t have it hosted anywhere but iirc the tl;dr is that they’re more or less independently reaching different conclusions as the two models are fundamentally incompatible.