If “natural born” has anything to do with sole allegiance, then the Constitution does address dual citizenship.
Natural born has nothing to do with sole allegiance, as discussed at great length by the US Supreme Court in 1898. It simply meant born in the USA, of parents here “in amity” with the US government.
Since we do not control the laws of Botswana, we cannot prevent Botswana from declaring all of us to be citizens of Botswana. But it wouldn’t matter if they did, because the US Constitution doesn’t discuss dual citizenship, nor use it to bar anyone from running for office.