@Francesco Camussoni​  : have you tried steps here: https://docs.databricks.com/spark/latest/sparkr/rstudio.html

In the script you have shared, I see you are directly using RSTUDIO_BIN , but I do not see any place where you have downloaded and installed rstudio (required)

To check the result of the init script , enable logging on the cluster, that way you can see the stdout and stderr of the init script from all nodes (note that since $DB_IS_DRIVER is used, the script is expected to run fine only on the driver node and the worker nodes will report failure, this is expected so when you enable logging on the cluster, if you see error that says DB_IS_DRIVER is missing, that just means you are checking worker node log)