If there is a shift to a new economic regime where inflation averages well over 2%, would central bank’s inflation targets have to be changed?

We can think that due to the appearance of multiple scarcities (labour, energy, commodities, etc.), economies will permanently move to a regime of higher average inflation, well above 2% (3%, more?). Central banks then have the choice: Between keeping the inflation target at 2% and conducting a continuously restrictive monetary policy; And changing the inflation target (3%?) to adapt it to the new economic equilibrium. Changing the inflation target comes at a high cost, with the central bank losing credibility and the risk of triggering a surge in inflation with a lasting loss of the anchoring of inflation expectations. But being forced to keep real interest rates abnormally high for a long time also comes at a very high cost.