The last sentence is exactly why you need to tax the big owners and corporations and not the workers, because they control most of the additional money supply in the profit-driven inflation.
(That being said, and as was noted, of course government can also run a surplus with the windfall tax, and that takes the money out of circulation entirely. However, as I explain above, inflation can be more complex, it might be money oversupply in only parts of the network, not the whole network.)
Where does the extra profit go (in the absence of windfall tax)? I doubt it goes to expanding production, because without windfall tax, you won't see demand change (and, btw, with windfall tax you don't have to estimate, you will directly see customers having more money to spend). So it will go into stock buybacks, real estate and other ways to inflate asset bubbles. These are seemingly easier ways to park money than to make actual real investment decision of expanding certain production.