How to use ColumnTransformer and FunctionTransformer to apply the same function to many columns, but separately?
I solved the problem by creating a wrapper around pd.cut, which then applies pd.cut using the apply method of DataFrame:

if isinstance(x, pd.Series):
    return pd.cut(x, bins_final, labels=labels, **kwargs)
elif isinstance(x, pd.DataFrame):
    return x.apply(pd.cut, args=(bins_final,), axis=0, labels=labels, **kwargs)