I think you are too focused on the words "nature" and "nurture". These words are imperfect labels, chosen for alliteration.
The "nature vs nurture" "debate" or balance (as few people really debate nature vs nurture except for the degree to which each is influential in a specific case) specifically refers to hereditary and non-hereditary (non-hereditary sometimes called "environmental") contributions to some trait.
You cannot understand the debate better by dissecting the words "nature" or "nurture". The "nature/nurture" phrasing is just a label, it does not contain intrinsic meaning besides being a cute linguistic phrase in simpler language; it's a lot like "survival of the fittest" in this way. It could have been labeled completely arbitrarily and there would not be any biological or underlying change in meaning. You could call hereditary factors "purple" and environmental factors "triangle" and refer to the "purple vs triangle" debate.
Importantly, estimating the influence of hereditary factors does not depend on the history of the evolution of those factors. Heredity is simply the portion of variation in people/animals/organisms that is explained by genetics. Natural selection is often an important contributor to changes in species, but evolution is influenced by other factors as well, like genetic drift, and "nature/nurture" is primarily about variation among individuals while evolution occurs in populations. The heritable factors that cause individual differences do not need to be adaptive.
There are of course different ways of defining what exactly it means to be hereditary, with some gray area around epigenetic factors, for example, but these must be addressed with more specific language in defining what exactly is meant by hereditary; you can't work backwards from the labels "nature" or "nurture" to understand what the boundaries should be, as those are merely labels.