The oil rigs aren't pumping because Biden shut them down. Biden is just the president. Besides all that, back in November a federal judge blocked Bidens oil lease block. All the oil leases are wide open again, and have been for several months.
Production wells pump when the oil companies say they pump.
Biden has no power to shut them down. Once federal leases are bought, they cannot be revoked. I would suspect that it will be overturned eventually.
Clearly oil companies have been told not to pump. It is proof that big oil is determined to keep prices high.