It seems that it is indeed the license used, that causes the Access Denied Error.
I was under the impression that Cloud Provider licenses were different from other licenses, but this is not the case.
Cloud Provider is an additional feature to the license, which is available in Standard, Enterprise & Enterprise Plus regardless of whether you are Cloud Provider or not.
However the license used on our B&R Cloud Connect Server is a rental license with a monthly fee of 4.50 euro for every VM in our repositories.
Currently I am not quite sure how changing to Enterprise will affect our rental license, as it will be customers sending their backup jobs to our repositories from their own B&R server.
The question I asked in this topic however has been answered. The license used by the B&R Cloud Connect Server is not sufficient to provide me with full RestFul API access.