Let's keep in mind that the study was only testing for something very specific (the diversity of HMOs), not for any direct benefits or general wellness like the press release article speculates. So the question isn't "should we expect rich people to have this good thing" (not actually tested), but rather, "should we expect rich people to be more likely to be exposed to areas with high biodiversity and low human impact", which were the main factors linked to HMO diversity. Which isn't necessarily the case.

The research article cites two specific indexes they tested as being linked to oligosaccharide diversity, the Simpson's Diversity Index of Vegetation Cover, which measures diversity of vegetation, and the Naturalness Index, which measures "how much human impact and intervention there has been in the residential area".

So those areas would likely be less conducive to oligosaccharide diversity since drier, colder, and more developed areas tend to have less biodiversity, though you'd have to check specific locales with the above indices to have a better idea.

The research article specifically mentions diversity of green vegetation, and not just exposure to any vegetation or other natural features, to be the biggest factor in its findings. In other words, not just being exposed to nature, but a diverse array of species of green vegetation, which would likely be more present in, say, a forest during spring than during the winter, or the desert.

So for the purposes of increasing the diversity of oligosaccharides in nursing women, simply being in nature at all is only weakly helpful. Certainly exposure to non-diverse nature is still good for the reasons you mentioned, just less so for oligosaccharide diversity.