You've got it right, the rising rates and tightening policy are basically to slow down the transmission of inflation (the good old inflationary spiral), they won't do anything much to address the original inflationary shock.
Basically it helps slow the economy, raise unemployment and reduce wage growth for a start.
Not a particularly pleasant way to deal with inflation but its pretty much what we have.
Using interest rates to control inflation is a blunt tool, which only really works on inflation with certain types of triggers - ie, when an economy is 'over-heating' leading to demand-pull inflation.
The major economies are definitely NOT overheating.
Rising energy costs and the knock-on impact for ordinary, every day products is already reducing the spending-power of consumers; the decline in discretionary spending. There doesn't need to be further brakes applied to the economy.
And applying further brakes won't reduce inflation.
Besides, if a brake does need to be applied to an economy, I much prefer the Keynesian approach to managing inflationary peaks. That is to raise taxation. It has a net benefit for society in that, once the inflationary peak has subsided, that additional tax revenue can be used to pay for public services and infrastructure that make the country better. If that taxation is applied progressively, then it acts as a mild redistributor, too.
All raised interest rates do is financially punish those with borrowings, whilst generaously compensating those with the most cash in banks, etc.
Finally, if you simultaneously have inflation with low interest rates, then that also acts to 'inflate away' the value of borrowings whilst eroding the value of huge cash assets held by the very wealthy.
