Negligence and “negligent homicide” are entirely different beasts.

Civil negligence would apply here but that would be limited to recovering damages.

The hacked website could sue to recover costs incurred, but what costs were incurred here? Maybe some wasted network bandwidth but that’s minimal.

You have to point to monetary losses caused by the hack. Only that would be covered.

Negligent homicide doesn’t apply because no one was killed.

Yes, obviously (and thankfully) no one was injured. I'm just using that as an example to show that Negligence is definitely considered in US criminal law ( https://en.wikipedia.org/wiki/Criminal_negligence )