ArcGIS 2.4.0: Can a geoprocessing service (custom tool) be published via ArcGIS Pro to be used in a web mapping application? I have been getting conflicting information.

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Can a geoprocessing service (custom tool) be published via ArcGIS Pro to be used in a web mapping application?

I am used to the traditional Desktop look/feel/functionality, but have been given Pro recently as my only option. After going through the model builder and running the geoprocess I only have the option to "share" as a geoprocess package or to share as a webtool; neither of which are actually working for me...pushing to a server nor to AGOL.

Thoughts/recommendations?

[Arne_Gelfert]

is this maybe a matter of privileges?

Publish geoprocessing services in ArcGIS Pro—ArcGIS Pro | ArcGIS Desktop 

You can only share a geoprocessing service with administrator credentials and connection type.