I think the division implied by the initial question of this topic is a false one. (A common one, though!) If a park is unnatural, that supposes that humans and human actions are unnatural and somehow apart from our surroundings. There’s the background idea that nature is a perfect state attained in the absence of humans. Really, it feels more like a kind of moral judgment than anything you can map more directly onto a real place.
I think it’s more useful to think of it in terms of ecosystems, or habitat, or biodiversity. An office building, a public park, and a section of undisturbed forest are all habitats which contain ecosystems, they will just host very different species and will have differing levels of biodiversity.
So I suppose the answer is that yes, I would consider cultivated areas to be a part of nature, because I believe humans and habitats constructed and shaped by humans are a part of nature too.
I think this also leads to more useful ways of thinking about the spaces we construct. If a university campus is an unnatural space solely for inhabitation by humans, then there’s less room for thought beyond the “nature / not nature” question. Think of a university campus instead as a space primarily intended for human activities and habitation, but host to other organisms as well, and you can work more intentionally to help improve the biodiversity of the space. You won’t be able to make an inherently high-traffic space suitable for larger and shyer species, but you can work to make it host a greater diversity of small species and act as part of a fragmentary habitat for flying species that will make good use of it.