So I did some looking into this. And I’d say it’s the same 的 but the usage of 的 seems to be broader than that.
Basically this usage somehow comes from the influence of Chinese, where in Modern Chinese it is used to make adjectives and connect nouns, similar to both の and な ,such as 我是高的男人。I am a tall man, or 那个有红色的车。 That is a red car. But this usage is modern, and 之 did this in Classical Chinese.
So in Japanese, this usage doesn’t start until the Meiji era and can be used both without な and as a generic connector. While you can do this with anything, it’s more common with certain words. And in this case it’s’s likely that this usage came about from that origin, but has just been solidified into an adverb from that. I can’t find anything specifically about this word though.