What if central banks really practised price level targeting?

Central banks have moved from an inflation target of less than 2% to a target of average inflation of 2% over a few years. They are therefore moving towards price level targeting: the price level must grow by 2% per year. When there has been a period of low inflation, it must therefore be followed by a period of high inflation to catch up with the target price level. This gives flexibility to monetary policies after a recession and normally helps prevent deflation. But by the same logic, after a period of high inflation there must be a compensating period of inflation below the 2% target if the behaviour is that of an objective price level. So where do we stand in the United States and the euro zone? What should monetary policy be in the future if the central banks really follow a price level targeting policy after the recent sharp rise in inflation? In the United States, a much more restrictive monetary policy would be needed; But in the euro zone, a neutral or expansionary monetary policy is normal, as the price level at the beginning of 2022 is below the price level target, excluding food and energy.