just a heads-up, in the middle of answering this I noticed just how long my answer has gotten (I'm kind of sorry for rambling so much but also, thank you for asking about my writing process. it means a lot to me.)

yes, I do listen to music while I write: no joke, I've literally got a yt channel for the playlists I create while writing (some serve the purpose of getting a feeling of the general mood of some of my stories, some are meant to kind of describe the individual chapters of multichapter fics, etc.)

I've got a playlists from when I was writing my Minkey Good Omens AU - it's called 'angel/demon au - mood/inspiration playlist' and contains edits from the original show and said show's main couple, there's also some songs that remind me of an angel and a demon falling in love (there's themes like forbidden love, star-crossed lovers and being in love but choosing not to act on it to safe oneself from the heartbreak before it even happens, etc.).

for one of my stories, I have a writing playlist as well as an official fic playlist for said fic. the songs in both playlists aren't necessarily all the same ones.

inspired by my Taekai fic 'the bet', I've created a playlist containing every song that gets mentioned in the fic itself (in a way, these songs even kind of describe the development of the story as well as that of the relationship between the two main characters).

the length of each playlist depends on how many songs I think fit the story.

for example, my Namjin fic 'keysmash' has a playlist with just six songs while I've also got a playlists with pre-made playlists (aka those yt videos that are already made up of different songs), so in a way there are probably a few dozen songs in that playlist.

for my current fem-Jeongcheol fic, I've created a playlist that's meant to be the setlist of GIRLNee (there are mostly just live versions of the songs that are part of the setlist in the fic so that I might be able to actually capture the vibe of these songs actually being played live and in concert)

to answer your second question (and I'm kind of sorry for how long this answer is going to be), I don't always listen to the group I'm writing about. sometimes, like I've said already, I go with a general mood which I want to capture in a certain scene or chapter. sometimes I much rather write while listening to something instrumental.

at other times, the groups I'm writing about aren't even part of my writing playlists at all.

all in all, what I listen to while I'm writing really depends on what I want to write.