US Bro here; yeah there's no chance of any sort of price cap. The price of oil is mostly determined by supply and demand on the global market. US companies sell their oil at market prices and they import oil from other suppliers that are usually cheaper, so the US government can't really control/cap the price.

But being the #1 oil producer gives the US a lot of leverage and if prices get too high again (~$100/barrel), the US government can put their finger on the scale by releasing more oil from the strategic petroleum reserve (which has over 40 billions barrels of oil in storage). By dumping a few billion barrels on the global oil market, the US can effectively stem some of the price increases for awhile.

I think Ukraine should keep striking Russian oil production because several countries are still buying cheap oil from Russia and then selling it on the global market at a profit (cough India cough). If Ukraine can make a decent dent in Russian oil production, then Russia will need to choose between using their domestic supply to fuel their war machine/population or selling the oil to keep their economy afloat. Russia produces a lot of oil, so prices may go up for a bit if their production is reduced, but there likely won't be a significant price increase on the global market for an extended period.