Inflation, page-50

And you've highlighted one of the main problems with monetary policy vs fiscal policy, which is the lags.
As you pointed out the raise in rates doesn't have an effect on those who have pro temp fixed rates, which we most commonly think of with mortgages, but they can be throughout the economic system.
So as I stated originally, all these rises for little effect in the aggregate. But the aggregate will have its day, we just don't know when, maybe AI could tell us.
In the meantime, govts panic and reach for fiscal levers if they dare. Put up some taxes if they dare.

Once inflation sets in it's like a self-fulfilling prophecy and is nearly always over compensated for. But sometimes govts get lucky.