Turning on the audio captions enables you to see the (often translated from Japanese) song titles. If you can grab that song title from the caption, we can point you in the direction of the original artist!
Please note that there is one artist that no longer distributes their music for free use. Thankfully, their tracks don't make up a lot of the soundtrack, so there's a good chance the song you liked isn't one of theirs, especially if it was a song you enjoyed in Adiaphoron.
Additionally, all tracks are converted from .MIDI using the soundfont mentioned in the credits, and will only sound exactly like the in-game version if you use .MIDI playback software with this soundfont.