Regulation is not separate from capitalism, but we aren’t talking about regulation. We are talking about state control, which is explicitly socialist. State ownership vs private ownership is literally the fundamental distinction between socialism and capitalism. In a fully capitalist system there can be no state ownership of means of production

capitalism requires contract law and the protection of private property rights, which requires a state, state-operated courts and police forces, whose existence cannot be subject to market forces as with private companies

Incorrect. Many corporations include arbitration clauses in contracts. This stipulates that disputes do not use government courts, rather using private third party arbitrators to litigate disputes. These courts are capitalist. Government courts are not capitalist (not saying they are socialist either).