As we have seen, even within the simple New-Keynesian model with cost-push shocks, the natural real rate of interest or the corresponding real interest rate gap alone is not a sufficient measure of the monetary policy stance. Moreover, it is far from certain what role the natural rate may play in models outside the NewKeynesian paradigm.
See  Lagarde, C. (2021), “Happy anniversary to euro cash!”, The ECB Blog, 31 December. 2/2  BIS central bankers' speeches