One of those elements that instantly makes a setting feel fleshed-out and well-realized to me is the presence of conlang, or constructed languages. It's dead impressive that the invented "chaos language" in NieR: Automata is custom-made just to deepen the series' often-haunting and sometimes-thrilling soundtrack.
It's so satisfying when a score is so well-matched to the material it's created to accompany that the two can become inseparably associated in your mind. Kids on the Slope is on the top of its game with regards to this.
Aria is another one of those shows that I love the idea of, but I've not watched a single episode of. Instead, I've thankfully run across its fantastic musical score.
I don't have any reservations about nerding out over games that I don't play at all. That's lucky, because Last Ranker is a double whammy, and soundtrack by Yoko Shimomura gets me going every time I hear it.
A lot of people will swear by working to music. I've personally found "slow noise" to be the way to go, and the soundtrack(s) to Hidamari Sketch fit this job to a 'T'.
Asian pop is catchier than the measles. To be fair, you could say that about just about any variety of popular music. But there’s something about Asian pop music in particular that feels like the strong elements of the medium have been reverse-engineered in a way that new compositions can have as wide an appeal as possible, making it stand out from almost anything else in the medium.