Nearly as I can tell, this may reduce oil prices by 3-5%, temporarily, maybe. So, instead of paying $4.20, maybe you pay $4. Suspending gas taxes does about the same price reduction, a bit more probably. It's not enough to make a difference.
When COVID hit, we could have bought oil on the cheap to fill up the SPR but didn't. That would have softened the blow to the oil markets some and government could sell some now to make a pretty penny. Buy low sell high is not a governmental ability.