I was tempted to downvote your post, but refrained, seeing how much effort you put into it. Sadly, it seems to miss the point of non-realism entirely, at least the way I understand it. I am not a realist, and have been quite vocal about my views here. Admittedly, they are rather more radical than those of many here. Mostly out of necessity, since once you become skeptical about one realist position, then to be consistent you have to keep decompartmentalizing until the notions of reality, truth and existence become nothing more than useful models. This obviously applies to normative claims, as well, and so cognitivism is not wrong, but meaningless.
if anti-realism is true, then it can’t also be true that we should believe that anti-realism is true
Consider thinking in terms of useful instead of true, it will magically remove all these internal contradictions you are struggling with. Sometimes it’s useful to follow the realist approach, and sometimes it doesn’t work and so you do or say something that an anti-realist would endorse. No need to be dogmatic about it.
Not sure about studies, seems more like a useful cultural thing, one of those traditions whose internal justifications have nothing to do with the reason they are useful:
https://slatestarcodex.com/2019/06/04/book-review-the-secret-of-our-success/
In this case it is probably about having a balanced diet with enough calories, vitamins, minerals etc. It is probably far from optimal, but a good-enough simple advice an average human can follow.