Hey Blue Prism Team & Community,
unfortunatly there is no way to authenticate at a Webservice with the currently logged in user using Blue Prisms WebAPI as the support told me. You have to store your credentials in the credentials section and select them directly from the WebAPI. There is no way to dynamically change the user to the currently logged in user.
This could be easily enabled by adding a Checkbox or an option to the WebAPI common authentication types which sets "UseDefaultCredentials=true" at the outgoing request.
For anyone else comming up with the same question my simply advice would be to not to use Blue Prisms WebAPI feature and better build up your own request using the HTTP Utility VBO.