The "add" option is certainly not immediately intuitive, since there's a clear duplication of the phrase "you have graced אתה חונן". It seems reasonable to expect that אתה חוננתנו was composed as a replacement for אתה חונן which includes the Havdalah parts. It's quite common in fact to see Piyutim composed as replacements for certain blessings over time ending up being printed in addition to the original wording, probably due to opposition (either rabbinic or communal) to abandoning the original wording.
There's actually a third option you don't mention for how to include Havdalah in this blessing which is to open with the ordinary אתה חונן line and then jump straight into the Havdalah portion without the extraneous opening line from אתה חוננתנו. An example of such an option is found in the Rambam's Siddur:
אתה חונן לאדם דעת, ומלמד לאנוש בינה, ואתה הבדלת בין קודש לחול, ובין אור לחושך... וחוננו מאיתך דעה ובינה והשכל. ברוך אתה ה', חונן הדעת.
Let's call the Koren-type option '1', the Rambam-type option '2', and Artscroll-type option '3'.
The Beit Yosef (OC 294) quotes the Orchot Chayim that you should not follow Option 1 since that would be changing the text of blessings improperly and instead you should follow Option 2 as found in the Siddurim of the Rambam and Rav Amram Gaon. But the Beit Yosef notes the custom is to follow Option 1 since it's essentially the same content and therefore isn't a problematic change. (Note none of them even consider Option 3.)
The Darkei Moshe there quotes opinions that Option 3 is indeed just a mistake and one should either follow Option 1 or 2. The Maharshal too cites these opinions.
But many later authorities felt that Option 3 was the custom and work to defend it. The Bach there says it's not a duplicate request since the first is referring to general knowledge (which God grants all of mankind חונן לאדם) and the latter refers to spiritual knowledge (which God only grants "us" חוננתנו). The Levush there writes along similar lines, and even argues for saying "וחננו..." twice, once for each type of knowledge. The Taz too defends Option 3 for Ashkenazim who understand "adding" in the context of requests for rain to similarly be strictly additive.
The Perisha defends Option 1, but the Magen Avraham says the custom is to follow Option 3.
So in your case it sounds like Artscroll is following the controversial "longstanding" custom, while Koren is accepting the old critiques and reverting to what appears to have been the "original" practice.
(I note the Mishnah Berura (294 sk 2) rules that, at least after the fact, one who followed either option has fulfilled his obligation.)