While currently, the US independence from "foreign" oil negates wild swings in domestic pricing, OPEC+ is still a major player. Russia and Saudis went toe to toe on who was going to blink first. While Saudi still thinks in terms of prices, Russia is thinking in terms of market share. Two competing principles. And it DOES affect world pricing. Eventually. Say the world oil supply can fit in a swimming pool. Add or subtract a teaspoon of water to a swimming pool on one end and the water will level out likely without even a ripple. You may not even notice. Like Iran getting into the oil game again. Too small for anyone to notice in the global sector by adding that amount to the swimming pool. A teaspoon or two. Take that same theory, and cut off supply by curtailing Saudi production. It's like taking a 5 gallon bucket and bailing out one end of the pool several times. You will see a noticeable difference on the far end of that pool, and when it levels out again, there's a lower level. Less amount (inventories fall), then prices go up. Let alone any refinery upsets or shutdowns. It's all a manipulation.
All in all, whatever affects DEMAND is what's going to determine the major amount of pricing going forward moreso than who's curtailing production.