Soy is kosher, and raw soybeans with nothing added do not require kosher supervision. Same goes for edamame (immature soybeans still in the pod). However, processed or cooked soy dishes must be certified by a reliable kosher agency or prepared in a kosher kitchen in accordance with the kosher laws. This is the case, even if the establishment is vegan.

Regarding Passover use, please see: Are Tofu and Soy Products Kosher for Passover?