Honest question: what type of insurance covers a catastrophic failure when "AI" is implemented like this?

There are very strict rules for when the government allows you to sue it. If it's never been tried before it's usually because it's not allowed.

That said, wrongful death / negligence is typically suable and many policies already cover that.

You're seeing all these half baked AI adoptions in government specifically because they're the entity most likely to be able to dodge paying for it when they've done wrong.

If you died, then complain.