This issue is addressed in ArcGIS Enterprise 11.2 and ArcGIS Pro 3.2.
The functionality is planned to be available in the core print service starting with the ArcGIS Enterprise 11.2 release. For the ArcGIS Enterprise 11.2 release, a custom JS API app is needed to make use of this. Please see the ExportWebMap specification in the REST API reference for more information once ArcGIS Enterprise 11.2 is released.