Do central banks really hope to eliminate inflation with modest rate hikes?

While announcing rate hikes, the Federal Reserve and the ECB are not talking about a shift to a very restrictive monetary policy. There is probably the hope of a soft landing: being able to break inflation without triggering a recession. But in reality, do central banks have such a hope or are they simply reluctant to say right now that monetary policy is going to get really restrictive? It will most likely take a sharp rise in interest rates to bring inflation back to the level desired by central banks: The price-wage loop that leads to permanent inflation is already present in the United States, and will gradually appear in the euro zone; Commodity producers have learned to obtain monopoly rents by keeping commodity prices high; this is facilitated by the shift in the structure of demand to goods, the war in Ukraine and the energy transition; the economic recovery in China in the second half of 2022 will once again drive up commodity prices. The question then is whether central banks will implement the necessary sharp rate hikes or whether they will give up the fight against inflation.