Which school of economic thought holds that the money supply chiefly determines nominal GDP in the short run and the price level in the long run?

Monetarism

Monetarism gained prominence in the 1970s through the work of Milton Friedman, who famously argued that inflation is always and everywhere a monetary phenomenon. A key takeaway of this school is the 'k-percent rule,' which suggests the central bank should increase the money supply by a fixed percentage each year to ensure long-term price stability.