Does Gradient Boosting perform n-ary splits where n > 2?
Gradient boosting can be applied to any base model, so doing it with a Quinlan-family decision tree (which allow for such higher-arity splits for categorical features) should make this possible.  However, all implementations of gradient boosted trees that I know of (and certainly XGBoost, CatBoost, LightGBM) all use CART as their tree model, so you won't get anything but binary trees.  (These GBMs do modify CART a little, e.g. in using histogram binning to reduce the split searches, but nothing as drastic as n-ary splits for categoricals.)