can tree-based models extrapolate with categorical independent variables I am aware of the fact that tree-based (machine learning) models struggle to extrapolate - see regression example here. I am only familiar with the concept of extrapolation for numeric independent variables. AFIK whether an independent variable is numeric or categorical, does not really matter for tree-based models. So can I conclude, that tree-based models can also not extrapolate for  categorical independent variables? Which model can extrapolate for categorical independent variables, if this concept actually exist for categorical independent variables?

Tree based methods predict the target (dependent) variable as the averages of the leaf values. The values in the leaves occurs in the training set, so you can't get an out of range output from the trees. This could happen even if the features (independent variables) are in their respective training data ranges.
But, a new value (extrapolation in your saying) for a categorical variable (IV) breaks the model. And this is not particular to tree based algorithms. With a new surprise category, you won't be able to execute a linear regression well (or at all).
