They don't need to. Interest rates aren't intended to control prices by creating an abundance of gasoline, but by creating a scarcity of dollars.
Yes, this can bring down gasoline prices. No, it doesn't mean gasoline gets less scarce in the process. It just means that each $1 gets dearer. It means that the price looks fine but you can't afford it anyway because your pockets are empty. The gasoline is still scarce even though the price is low. That's what they can do, and what they are doing.
And it's best to understand that, when interest rates go up, the first pockets to empty are emptied by falling asset prices. Stocks, bonds, and real estate. That's why high inflation numbers are bad news for assets, even though they'd intuitively seem like inflation hedges.
There are these products that no matter how dearer $1 gets - you will absolutely buy them. You can't destroy demand on these products like what you're describing. You and your family could literally die without some of these products. And no raising of interest is going to help that.
A century ago, a loaf of bread cost only a nickel and that's not because people ate less or because food supply was more plentiful or demand more elastic.
But even setting that aside, interest rates operate on aggregate demand which is averaged across all goods, just like inflation is.
Raising interest rates isn't going to impact companies just charging more for what they sell.
The only thing that stops companies from charging more is individuals unwilling or unable to pay the higher price.
Can you turn off your spending on food?
Edit: from the report:
> Increases in the shelter, food, and medical care indexes were the largest of many contributors to the monthly seasonally adjusted all items increase.
Can't turn off spending for food and medical care if you want to live
I live in a high poverty city with wondrously low "unemployment" but a high number of people who don't have jobs. The answer: if you can qualify for a job, yes you can get a job, but a lot of people do not qualify for anything worthwhile, so why try?