Reading about the cultural and social importance of bathing throughout Chinese history (because I am exactly the kind of person who spends hours reading about the cultural and social importance of bathing throughout Chinese history for no particular reason on a Tuesday night) and obviously now I'm imagining the sects all lowkey competing with regards to their public baths -- or at least the ones meant for visiting disciples and dignitaries.
The Jin are obviously doing The Most and being incredibly tacky about it. The floor of the bath is made of gold tile that dull super quickly and the whole tub needs to be frequently drained so the tiles can be deep cleaned and polished, and of course once they're shiny they reflect light up and through the water in a way that's actually really distracting. The bath bean has crushed pearls and seventy four different types of flowers in it. The benches are intricately engraved and inlaid with gems in places that pinch your butt when you sit on them.
The Nie have a natural hot spring that they have turned into their main public bath. The massive cavern houses a number of varying-sized pools, some of which interconnect and others of which are freestanding. The free standing pools are typically treated with different soaks to give the water various medicinal properties (most often for things like muscle aches or minor injuries, but also for skincare and such.) I imagine the Nie recipe for bath-bean would include animal fat and pancreas, making it very rich and cleansing.
Part of me wants to say the Jiang would just bathe in the lake but that seems cheap to me, so instead: Through a combination of well-placed pipes and clever array work, the Jiang bath house feels like a mini indoor rainstorm, with water falling in thousands of warm droplets from the ceiling above to fill the pools, which are more shallow that a typical bath would be. There are built-in overhangs you can sit under to get out of the "rain" while still being in the water. If requested the rain can be "turned up" and the lights dimmed, and cymbals crash so you feel like you're really standing out in a raging thunderstorm, which some people find incredibly soothing and others find terrifying. I can't think of anything unique for the bath bean other than lotus flowers but I do think, given the proximity to the river, that mud wraps would be a common treatment offered.
The Lan... probably have the worst public baths, actually. They may not even actually have a public bath at all. If they do have one, it's not meant to be a place of luxury or entertainment, although of course it would be tastefully decorated and comfortable. Rather they'd find some way to make public bathing less about socializing and more about silently meditating while pretending you aren't surrounded by other naked people. I guess the cold springs kind of sort of count as a public bath but not really. Bath bean smells distinctly medicinal, but obviously whatever is in it works, because the Lan all look Like That.
The public bath in Qishan stopped being a popular attraction when Wen Ruohan stopped having visitors, but for years their bath was one hell of a marvel. Massive, bronze statues of phoenixes would be heated until glowing-hot and then lowered into the stone tub, filling the air with thick steam. Patrons would sit around the room on their benches, sweating it out until the statues had cooled enough for the water to be safe to enter. If you wanted a cold bath, the adjoining room was also home to a massive bronze statue, this one of a dragon that sat in the center of the tub and poured cool water out of it's mouth. Bath bean was made with plant ash rather than rice or soybean powder, and the water was all treated with volcanic ash.
And, because I am Me, the Wei sect: I'm imagining a dark hall deep in the cave systems, the floor lined with man made in-ground pools of varying sizes not entirely unlike the Nie baths, however these pools aren't connected to an outside water source or each other. There are illusion arrays carved into the walls that send out glowing, ghostly shapes of fish and otters and other river creatures swimming through the air. The pools are filled through overhead pipes that pour water, oils, and herbal mixtures into the pool, and each pool has access to it's own set of labeled levers, so a person or group of people can customize their bath while they're having it, adding more cool water, hot water, or various add-ins. The bath bean is more of a paste due to the addition of a ton of collagen. (They get it from the kitchen's bone broth. The bones are not human, but that doesn't stop visiting disciples from scaring each other about it. Don't piss off the Yiling Louzu or you'll end up in the soap.)
