You are correct that a Demand shift does increase Q. supplied (not "Supply")
But this article is about which comes first in macroeconomic activity -- Aggregate Demand (as Keynesians insist) or Aggregate Supply (work effort and production of goods, those then allowing trades and "demand" in general to arise).
The latter is what Austrians and other free market economists argue. And it's true that government can destroy incentives to work, invest and be productive (meaning less Aggregate Supply is created).
The damnable homosexual Fabian socialist Keynesians argue that an increase in quantity demanded will automatically be followed by an increase in quantity supplied as production will ramp up automatically to chase those extra dollars.
The Austrian school (the supply siders, not the modern ones who follow the lockdown theories of the most infamous Austrian paper hanger) will not necessarily be the case if the supply chain is disrupted.
The Keynesians, if they are honest, will counter that while this may be true in the long run, it is the short term that matters because (to quote their guru) "in the long run, we are all dead."