You'd still have radiative heat transfer, even if there is a vacuum between the panes. For a given budget, you're probably better off adding more regular panes.

Aren’t new windows often coated with something opaque to IR, that way they keep heat in during winter and don’t heat up like a greenhouse in the summer?

Those are low-emissivity coatings. Very effective in reducing radiative heat transfer. This is why the glass in a vacuum flask is silvered: metals have low emissivity. These coatings aim to have low IR emissivity while still allowing visible light through (IR light gets reflected, instead of absorbed/emitted).

My point was only that a vacuum gap is still not a perfect insulator, so it's an economic trade-off.