@jinmohl @LLENN
Awayuki is in-manga.
Awayuki isn't a band, it's the artist name for Awaji Yukina-san. (Her name is explained in chapter 02, apparently she was in charge of the band performance in chapter 01)
Since the suggestion for the sound of the band in Ch 01 was to listen Oriental Journey by AUNJ Classical Orchestra that might give one idea about her style.
(In chapter 2 it is also suggested that you should probably listen to HIDE x HIDE - but there's an errata about which shamisen they use in Ch 07)
In Chapter 7 there's also a reference to "Green and" by "SUN[kanji]" being an inspiration for the music in Ch 01 (only the flute, I think, but that in turn might have been supposed to have been inspired by Awayuki, so..)
(There might also be more music suggestions said in the end of Ch 06, but that page isn't translated so I can't say
(Not too hard to predict is that since it's a manga-creation and that it has been so prominent, that we'll get to see more of Awaji Yukina later on.)
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Also, since I pinged you - thank you for your hard work and the nice commentary.