Regulatory capture is using the state's power. The state is the one with the power. Rent seeking is the same. Hiring goons is illegal. If you're willing to include illegal things then all bets are off. But from your list of non-illegal things, 100% of them are the state using its power to wrong ends.

> The government itself uses money to do those things. Police don't work for free, prisons aren't built for free, guns aren't free.

Yes, but the point about power is the state has the right to lock you up. How it pays the guards is immaterial; they could be paid with potatoes and it'd still have the right. They could just be paid in "we won't lock you up if you lock them up". However, if Bill Gates wants to publicly set up a prison in the USA and lock people in it, he will go to jail. His money doesn't buy that power.

So, no. The state doesn't have power because it has enough money to pay for a prison and someone to throw you in it. People with money can't do what the state does.