Hello @ChristophKiefer-9885,
You can install R-Studio as a custom component.
Important note that we will not be able to provide support on functioning of a custom component.
Here is a 3rd party content which suggests that solution - Installing R-studio on Azure HDInsight.
Disclaimer: This response contains a reference to a third-party World Wide Web site. Microsoft is providing this information as a convenience to you. Microsoft does not control these sites and has not tested any software or information found on these sites; therefore, Microsoft cannot make any representations regarding the quality, safety, or suitability of any software or information found there. There are inherent dangers in the use of any software found on the Internet, and Microsoft cautions you to make sure that you completely understand the risk before retrieving any software from the Internet.
Hope this helps. Do let us know if you any further queries.
Do click on "Accept Answer" and Upvote on the post that helps you, this can be beneficial to other community members.