--- Arrow 1 ---
Rikyu has helped with healing Iyo, and is now conversing with Nobu. She hasn't seen Nobu since the incident at Honnoji. Nobu isn't sure if Rikyu is even a Servant, but more importantly, wonders how the hell they could be a woman, although Gudao wonders if that's really something Nobu is in a position to ask. Rikyu says the form itself is trivial, but since this is how it is right now, she doesn't have much of a choice. Rikyu gives you all some amazing tea to help you calm yourselves after this, and then suddenly says your time is up. The tea must have been poisoned, in a way that went straight to the Servants' Saint Graphs, because Okita suddenly feels really sick. Except...Okita didn't drink any tea. Nobu surmises that it's not the tea (which she and Majin drank) that's poisoned, it's the very air inside the building, and so Rikyu once more offers Okita a cup of tea to ease her staying.
Basically, the space here is filled with a poison you can't see, and which would take out even a Servant if left untreated. Rikyu's tea does wonders in treating it and keeping people healthy though, so it's fine. That's also why there's a vending machine outside, to attract people to buy the health potion tea, but she hasn't had much luck with that. Okita then thinks Nobu must've been able to see the poison, since she drank the tea right away, but Nobu says that if she was that cautious there's no way she would've died at Honnoji. Gudao, on the other hand, is a dumbass for just gulping it down immediately.
More currently, Rikyu was summoned here before you were, and she noticed this is a place where even Servants have a hard time maintaining their existence. She had to set up the teahouse, which is her Bounded Field, and create tea with Magical Resistance-bonus to be able to operate outside. Still, even if she were to go outside, there's the wolfmen roaming about. Majin doesn't care much for this exposition, and just wants to eat, and so Rikyu brings out the meal, which seemingly consists of a bunch of "tea nobbu".
Okita:
Alright, that's it! This singularity is just another one of Nobu's messes.
Let's just go home Master, nothing good will come of this!
Nobu:
I don't think there's ever been a Singularity that was my fault.
No wait, was there one?
Rikyu explains that the tea nobbu are mysterious creatures who wander the land, but take kindly to being given tea. Still, what are they even doing here? Well, Iyo can explain that, now that she's up and about thanks to the magical tea. She reintroduces herself as Iyo, second Queen of Yamataikoku, and the wolf-headed man you fought earlier as the King of Kuna (lit. "dog people"), the Beast Sword himself - Kukochihiko.
The scene changes to show Kukochihiko somewhere else, also drinking tea to keep himself maintained in the land, but complaining about the taste. Another person is there, saying they don't care if it tastes good, as long as it keeps them alive. But if Kukochihiko wants to be swallowed by the mud of the land, he's free to stop drinking the tea. The mysterious person asks how it went before, to which Kukochi relates his meeting with Chaldea. Even having been told about them, the mysterious person doesn't believe anyone can maintain themselves in this place, even if they're a Heroic Spirit, without being swallowed by the mud. However, Yamanami, who is also there, doesn't think it's gonna be that easy. After all, he would know, having fought with both Chaldea and Kukochi before.
Kukochi berates Yamanami for lacking loyalty, referring to the finale of Yamataikoku when he betrayed Serizawa. The mysterious person says they do not care about this squabble, because they know all too well the farce that is loyalty. Yamanami is to do as he is told, and if he means to betray them, then he does best in knowing what that would entail. But Kukochi wonders what they're gonna do about Chaldea now.
???:
I'll just meet them head on.
I, here in this new Yamataikoku, Jibu-no-shō.
Or should I say, Ishida Mitsunari.
(TL note: Jibu-no-shō is actually the title of a court official position, but ever since the edo period it came to basically always refer to Ishida specifically.)
--- Arrow 2 ---
You think back to the events of Yamataikoku and meeting Kukochihiko back then (he was that skeleton-looking creep that possessed Serizawa). He should've disappeared back then, but him being back here might have to do with what this place is. Iyo explains it along the lines of this being a sort of limbo, between the actual realm of the dead and Yamataikoku, where dead souls come on their journey to the afterlife. Except, it's like, offset, or not where it's supposed to be. So Iyo's job this whole time has been to help the souls stuck in this place, having lost their way, into the afterlife. At the same time, it seemed that the spirits of the haniwa nobu from last time were also stuck here, and that they began to live here instead. Also, since this is the road to the afterlife, that means the child you've been taking care of is actually...
She quickly introduces herself as Shusha (or at least she thinks that was her name), and she explains that there was something very important she had to do and somewhere she had to go, but she can't really remember. She couldn't go alone back then, but then she ran into Iyo who said she would help. Iyo thinks she might mean to go to a realm far away, called "Nirai Kanai" (TL Note: in a group of Okinawa and Amami religion called Ryukyu Shinto, Nirai Kanai is both the place where all life originates, the equivalent to heaven, and where the gods live). Obviously, you agree to help, and the tea is set to work for at least another day. Of course, it'd be too much of a hassle to come back here to refresh the effect, so Rikyu will simply accompany you, and so will the teahouse.
This is the Rikyu Scramble, the great goal of Rikyu while they're here to reach out with their way of tea to many more people, but in a totally new way. Suddenly, the teahouse flies into the air. This singularity is made up of islands separated by an uncrossable sea of mud, so the GO-AN (or "GO hermitage", as it would be translated) as she calls it will
move around instead. They make a reference to Hideyoshi's "portable tea room", but Rikyu says that was merely a prototype for this.
Just one more thing: when you want to use this place, you have to pay up. Even though she's also a Servant and needs your help, this is non-negotiable. People just don't respect what comes to them for free, and this is a fundamental principle of human civilization since ages past. However, rather than pay with money, you'll collect ingredients and tools to make tea, so that Rikyu can eventually make the perfect cup of tea which will maintain you here with just one cup.
Also, before you leave, Iyo asks about Himiko, saying this would all be done in a jiffy if she was here, and then getting all bubbly and whatnot thinking about it, but unfortunately you're not able to establish communications with Chaldea at the time.