It's not that the invention of LLMs conclusively disproves Chomksy's position.
However, we now have a proof-of-concept that a computer can learn grammar in a sophisticated way, from the ground up.
We have yet to code something procedural that approaches the same calibre via a hard-coded universal grammar.
That may not obliterate Chomksy's position, but it looks bad.
That's not the goal of generative linguistics though; it's not an engineering project.
The problem encompasses not just biology and information technology, but also linguistics. Even if LLMs say nothing about biology, they do tell us something about the nature of language itself.
Again, that LLMs can learn to compose sophisticated texts from training alone does not close the case on Chomsky's position.
However, it is a piece of evidence against it. It does suggest, by Occam's razor, that a hardwired universal grammar is the lesser theory.
How do LLMs explain how 5 year olds respect island constraints?
I don't have the domain knowledge to discuss that.
If you don't know what a syntactic island is, perhaps you're not the best judge of the plausibility of a linguistic theory.