>What does “state level powers” even mean?
In this case espionage and surveillance, traditionally domains of the state.
>What do you think they do that’s so above-and-beyond what a non-government organization should be able to do?
They're not subject to privacy legislation and limitations that the police is. There's a concrete exapmle of this, commercial storage of license plate data in the US is largely unregulated, so police units that have legal limitations on how long they can hold citizen data simply go to the private market and buy that data from those firms. That kind of circumvention of the law and outsourcing of responsibility is probably a large part of the Palantir business model.
Seems kind of insane to take your tax payer money and use it to buy surveillance data on you, a good chunk of which probably isn't even legal to otherwise collect and completely undermine the rule of law and democratic control of policing.