Exactly, and the advantage is that checking that the problem is "formalized" here is essentially isolated to verifying that the final theorem statement matches the claim. If there are no 'sorry's and the program compiles, then it has been proven. That's the point of Lean.

As the recent "proof" of the Collatz conjecture shows, that's not enough in an adversarial context. Human mathematicians don't submit proofs that take advantage of soundness bugs in Lean. AIs do.

Each word of your answer is carefully chosen. I'll add one sentence though: you let time do its job.

Of course there may be errors in lean, of course AI can take advantage of it, of course "carefully" is full of errors. So the only thing left is waiting to see if the result holds. And yes, it may take 30 years...