I guess there is a distinction here; one is either choosing to take the outlier value and set it to NA/missing, and leave it at that; or go an extra step and impute what the value may have been.
package mice is popular for missing values imputation i.e. the second step.
geom_boxplot documentation shows how it considers values greater than 1.5*IQR away from the outer quartiles to be outliers.
What does "compact" represent in this example if I may ask? I have only one column that is to be processed it is called SupDem and the name of the dataset is df_a.