I am not an “insider” in the industry, but my understanding from observation of, yanno, bookstores, libraries, etc. is that the categories Children’s, Middle Grade, Young Adult, New Adult, Adult are mainly intended to describe the demographic the work is marketed to.
Usually and coincidentally (but not 100% as a rule) these also happen to correspond to the ages of the characters.
So, the author has to consider (in describing or pitching the work) which audience they believe will be most likely to buy/read that story about those characters. Then, a publisher would have to consider whether they agree.
I do know from articles about works that sometimes an author initially imagines marketing to one category, and a publisher suggests aging characters up or down to market the work differently. I don’t know how common that is, though.
“New Adult” is usually for and about people adulting for the first time, could be college in some cases, but more likely first jobs, first serious relationships, first time living alone, etc. But, it’s most often going to be about characters who do this at the typical age within a society.
So even if a 14-year-old character is “adulting” the work wouldn’t necessarily be found acceptable in publishing as a New Adult work, because that’s not the typical experience for the demographic. That’d more likely be YA (I’m guessing), for example, because there’s the balance of the younger teen but the more adult situation.