Serus (serus_caprakus) pointed out in the "All Living Ghost Netplay" Discord Server that "in Nazrin's, Aunn's and Seiran's story, Yachie and Saki will play theír own themes for a second before it gets replaced by Zanmu's theme".
This sparked my curiosity to see if there are any music oddities in Unfinished Dream of All Living Ghost and after checking each route, I realized that it becomes very messy once you try to understand how the song assignments are done.
As a starting point, let's take the trivia mentioned by Serus above. As you can see the pattern there is "pre battle theme" > "own boss theme" > "Zanmu's theme". It seems that during Seiran's route, there exists a similar music oddity in stage 4, excepting that there is no pre battle theme, instead Tsukasa's theme can be heard at first, followed by Suika's theme.
Normally, all boss themes are preceded by a pre battle theme. There are few exceptions to this (besides the one mentioned earlier): stage 1 and 2 from Yachie's route, stage 3 from Biten's route, stage 1 from Saki's route and all stages excepting the last one from Yuuma's route. In this cases, the bosses own themes start directly at the beginning of the stage.
While some stages play their own boss theme, other play either Reimu's, Marisa's or Suika's themes and there is absolutely no pattern to this. If you read the descriptions of these three themes in the Music Room, it says that The World Is Made in an Adorable Way is "Reimu Hakurei's and the early stages' theme", Magical Beast Scramble is "Marisa Kirisame's and the mid-game stages' theme" and The Oni on the Perpetual Mountain is "Suika Ibuki's and the end-game stages' theme".
If you were to look at where these songs replace other bosses themes, you could deduce that "early stages" are stage 1 and 2, "mid-game stages" is stage 3 and "end-game stages" is stage 4. What about stages 5 and 6, aren't those end game ones? All stage 5 play their own bosses' themes; Suika's theme can be heard only in Hisami and Zanmu's routes, where she actually is the stage 5 boss, so that's not very helpful. Suika is the last boss from Biten's, Enoko's and Chiyari's routes, but she plays Zanmu's theme. Even stage 6 Reimu from Zanmu's route plays Zanmu's theme instead of her own. The only one who plays her theme for the entirety of the stage 6 is Yuuma from Ran's story.
From stage 4, most characters play their own themes, excepting Mamizou from Aunn's and Nazrin's stories, Tsukasa from Seiran's story and Reimu from Biten's, Enoko's and Suika's stories, who all play Suika's theme.
From stage 3, some characters would play their own themes, but others would play Marisa's theme. These are Reimu from Marisa's and Aunn's stories, Mamizou from Sanae's story, Seiran from Nazrin's story, Nazrin from Seiran's story and Ran from Rin's story. As a weird exception to all of these, Yuuma from Mamizou's story would play Suika's theme instead.
Stage 1 and 2 bosses, would normally play Reimu's theme. During Hisami's and Zanmu's routes, the stage 2 bosses play their own themes instead. Also, from Yachie's, Saki's, Yuuma's and Suika's stories, both stage 1 and 2 bosses play their own themes instead of Reimu's theme. As an exception to all of these, the stage 1 and 2 bosses from Mamizou's route actually play Mamizou's theme (the player's theme, not the bosses theme or Reimu's theme).
This leaves Ran, Aunn, Nazrin and Seiran to not have their themes heard anywhere during story mode.
As you can see, it's very messy, there is no clear pattern to anything. I hope this post will be a good reference to some of you later on instead of wasting your time trying to piece together what songs play where. Also, to clear this up, I've checked in both ver. 1.00a and ver. 1.10c and nothing was changed in terms of music assignments between versions.