If we turn St Petersburg into rubble, I doubt anyone will be worrying about a few trifling conventional weapons. NATO and Russia go at it, and we're all just sitting around next month waiting for the Chinese, Brazilians, Indians and South Africans to sort out who is responsible for which relief efforts.
Actually, now I think about it, that quad will probably be far more concerned with determining the disposition of the remaining NATO/Russian warheads. So even relief efforts might be impacted by their more pressing concerns.
In any case, the world would just be a mess for a good long while.
All that said, you are absolutely right about "spoils". No one is gonna be thinking about "spoils". Probably top of everyone's list of questions will be, "How many warheads are left? And what remnants of NATO or Russia control them?"
We're talking about two groups who would have conclusively shown they are perfectly willing to use their nuclear arsenals to achieve their goals. That, combined with the fact that their goals would become a whole lot less lofty overnight makes me think the world would become a very precarious place.