DecisionTreeRegressor under the hood of GradientBoostingClassifier
After reading through more of the documentation I found the section that covers the classification case. It can be found here. Additionally this statquest was very useful.

1.11.4.5.2. Classification
Gradient boosting for classification is very similar to the regression case. However, the sum of the trees
is not homogeneous to a prediction: it cannot be a class, since the trees predict continuous values.
The mapping from the value
to a class or a probability is loss-dependent. For the deviance (or log-loss), the probability that
belongs to the positive class is modeled as
where  is the sigmoid function.
For multiclass classification, K trees (for K classes) are built at each of the  iterations. The probability that
belongs to class k is modeled as a softmax of the
values.
Note that even for a classification task, the
sub-estimator is still a regressor, not a classifier. This is because the sub-estimators are trained to predict (negative) gradients, which are always continuous quantities.