One thing I noticed is that place the stalker ends up in on the final page appears to be the school from the previous chapter, but before Ouka gets chopped up. The implication seems to be that they're the one who killed Ouka in that particular timeline.
More notable details:
We've seen three (potentially four) different chihayas now based on hair and clothing choice. Schoolgirl, mafia! vest, tuxedo and possibly stalker.
Ouka has different flowers in her hair in the first chapter, the ghost ouka in the opening of second is wearing a ring, but they otherwise seem to be the same.
Tuxedo Chihara from the first chapter didn't start out with a blade, but a gun, unlike the other chihayas.
This is indeed channeling, and quite strongly at that, the premise and imagery of Yami to Boushi to Hon no Tabibito, an important but not-much-talked-about-these-days early (though post-Utena/Sailor Moon/Marimite) yuri anime, quite possibly the first to ever have as its central overarching theme an explicitly romantic relationship between two girls - though it would soon be overshadowed by Kannazuki no Miko only a year later.
Stoic TDB (tall, dark, bishoujo) with a sword jumps through parallel worlds searching for her adopted sister with whom she shares more-than-sisterly feelings, including an Orient Express-style train situation.
But indeed, my first thought at this was indeed "Is this a Yamibo fanfic". Except the setting is a bit more mysterious. I suspect there are at least two Chihayas... though I suspect it's actually three!