The webpages are entirely generated without a binary build (a build from scratch is quite daunting as stated in the project readme) of Lean artifacts. See https://github.com/anthropics/fermats-last-theorem/blob/main...
The Lean system has already experienced soundness bugs.
The question is, will future generations doublecheck this proof with a frozen Lean system of today? There is a lot of incentive in having LLM's be the first to find high profile theorems like this.
I wouldn't vouch my hand in fire in asserting the validity of this gigantic proof.