Warrior’s Path (Shitō) is Kudo’s art: send a body through architecture. He spends it on Hakuri. The Volume 11 synopsis already says Kudo dies for Hakuri. Headquarters is the building. The Storehouse is the other way through a wall. Kudo’s way is a person thrown as a key.
A death the plot still spends
The deaths page keeps him on the list of named fates. This room is the technique so the sacrifice has a verb. Official chapters: VIZ / MANGA Plus.