Raising interest rates takes money out of the economy…. So that helps with inflation…yes, that hurts, I get that… the argument is that the pain is far less than continual inflation .
But also, inflation weakens your currency making imports more expensive. High interest rates encourages people to invest in your currency strengthening it and reducing inflation.
'Taking money out of the economy' only acts as a deflationary measure when the cause of inflation is of the 'demand-pull' kind. This isn't a demand-led inflationary pressure.
Higher interest rates do attract external investment (over investing in other countries), which creates a heightened demand for the currency, increasing its value which, as you say, makes imports less expensive, so lowering inflation. However, as I've been at pains to explain, that only works when a country raises interest rates in isolation. When a country raises interest rates and other countries follow suit, the initial, brief uplift in currency value evaporates almost immediately. And this is what is happening. You're back to square one, but with higher interest rates and added costs onto businesses (who in turn pass this increased costs onto consumers, creating its own inflationary pressure)
The core drivers of this inflationary spike are, on the face of it, temporary.
Supply-chain disruption caused by Covid is slowly working through (although some sectors are taking loger to normalise - eg, semiconductors)
Fuel cost surges have been driven by Russia's actions (initially strangling gas supply to Europe in Q3/21 then invading Ukraine), and you'd hope this wouldn't drag on that much longer. But we've had the surge, and prices won't keep increasing (even if they remain high but stable, the inflation factor disipates)
Food price increases, again mostly leading on from the invasion of Ukraine
The fly in the ointment is that workers are justifiably demanding pay rises commensurate with inflation rates. This acts as a further inflationary pressure, although most usually a decreasing one.