What determines inflation in the long term?

In contemporary economies, the relationship between money and income (nominal GDP) is no longer stable in the long term. The expenditure logic has given way to a portfolio choice logic , where money has a stable long-term relationship with the value of different asset classes (equities, bonds, real estate, etc.). If , in the long term, money supply growth now influences asset prices (share prices, long-term interest rates, real estate prices) and no longer goods and services prices, it remains to be understood what determines inflation in goods and services prices in the long term. For the proponents of neo-Fisherism, it is the level of the nominal interest rate chosen by the central bank. It is also possible that a self-fulfilling equilibrium is at play, where inflation simply stabilises at the expected level. No longer knowing what determines inflation in the long term is a serious problem for central banks (how do they influence inflation in the long term?) and investors (what mechanism will bring back prolonged higher inflation?).