I understand that the Dark Side and Darker Side have a distinction between Duplicate Moons and No Duplicate Moons for the sake of the extra moons that become available in the shop after the credits roll.

My question concerns any% or World Peace. None of the runs I've seen thus far have included a moon purchased from the shop in any kingdom besides Wooded Kingdom. Is there a rule that prohibits purchasing a moon from another kingdom, is it just an unwritten but followed rule, is it just not fun to watch, or has simply no one tried it?

I'd say, variables (if implemented once) are not set-able for only one explicit category. So they are there for all of them. Even if unused, you can't switch them off.

I understand that. That mainly applies to the shop moons that are made available after the credits to determine whether grinding coins to purchase a bunch of moons is allowed or not. But that isn't even an option in any% or World Peace. There aren't even really duplicates. The moons "Shopping in Steam Gardens" and "Shopping in Mount Volbono" are, by naming convention, two different moons in two different Kingdoms. Not like having 11 moons from "Shopping in Steam Gardens". But no runs I've seen in the relevant categories have purchased a moon from a different kingdom. So how does this clause apply in that case? Are they considered duplicates by the community, or are they fair game?

You can buy as many moons as you want in Any%/World Peace. The only moons bought in Any% are in Wooded and Snow because buying a moon would be slower in most kingdoms.