Ok, when trying to create a second project, I realized what was wrong.
When creating a subpackage for a new project, if you use the context menu in the Repository view, it will only create the package in the repository, without the authorizations, which then triggers the issue.
If you create the subpackage while in the System view however, everything is created/granted, and you can then create the XS project without problem.
It might be a good idea to add a warning about this distinction in the documentation, to avoid others running into the same issue 