Kanako did say that Yuiman is a fellow god from her "hometown", but does that mean Kanako is also from the Yuiman country? 🤨 But the word for it goes all the way up to region level.
I think more likely is that Kanako and Yuiman are fellow kunitsukami – if I recall Yuiman's legend correctly, there are like about 70 other countries (one of which might be Kanako's) until the protagonist reached Yuiman – and when the amatsukami descended to rule the land, Kanako got a much better deal than Yuiman?
By the way, soap in Japanese is "salty stone".