@Soapmaker333 -- "...everyone also says you need surfactants for shampoo. Clearly not. I don't see any surfactants here at all...."
I see some misunderstandings here, so time for some clarifications.
Coconut oil saponified with KOH (potassium cocoate) is soap. So soap is the main cleansing ingredient in this product.
A simple way of defining a surfactant is any chemical that acts as a chemical bridge between water INsoluble chemicals like fats and water. This chemical bridging causes fats (or other water insoluble chemicals) to become more water soluble.
Surfactants (surface active agents) include emulsifiers, solubilizers, soaps, synthetic detergents, and many other chemicals.
Soap is a surface active agent in that it can emulsify or solubilize fats so they become more water soluble, hence soap is a surfactant. Potassium cocoate is a soap hence it is also a surfactant.
A surfactant that is good at cleaning surfaces is called a detergent. Soap, including this potassium cocoate, is a surfactant that cleans, hence soap is a detergent.
Not every surfactant is good at cleaning things, however, so it's good to remember that all detergents are surfactants, but not all surfactants are detergents (cleansers).
@AliOop -- KOH soap can solubilize / emulsify small amounts of fats, so you're probably right they're using only tiny amounts of each oil to keep the total amount low enough the soap can handle the fat load.