the source of inflation isn’t all that relevant in terms of interest rates though… they aren’t going to solve the problem (rate changes never do) but they cool the rest of the economy in aggregate and cut off wage-price spirals
it doesn’t really matter if you’re paying 20% of your wage in energy bills if the remaining 80% still allows you to buy whatever you want. inflation only comes down when discretionary spending slows
rate hikes don’t target inelastoc spending like food and energy; they target things like home and car purchases which reduces the amount of cash sloshing around