What does central bank independence and credibility mean today?

In the usual literature on monetary policy, central banks are: Independent: because , in the medium term, monetary policy only affects inflation, there is no need for central banks to coordinate with governments (monetary policy does not need to be coordinated with fiscal policy); Credible: economic agents know that the central bank will not use unexpected inflation (in goods and services prices) to stimulate activity and drive down unemployment. As a result, expected inflation remains equal to the inflation target. What has become of these notions today? Given that central banks are implementing helicopter money (monetary financing of public transfer payments), they are taking part in governments’ fiscal policy. So they certainly cannot be independent; As the correlation between the unemployment rate (economic cycle) and core inflation has become very weak, by construction credibility with respect to inflation in goods and services is assured; But unlike the assumption made in the usual model, what monetary policy controls today is inflation in asset prices and not in goods and services prices. In order to be credible, central banks must therefore refrain from using inflation in asset prices to stimulate activity, which is clearly not the case. At this juncture, it has to be explained why rising asset prices stimulate activity (is it inflation in asset prices or unexpected inflation in asset prices?). It has to be admitted that central banks are no longer either independent or credible. This is only a problem if: The helicopter money corresponds to inefficient public spending; Inflation in asset prices reduces well - being.