The option to enable Server Object Extensions and Server Object Interceptors for services published from ArcGIS Pro does not exist in ArcGIS Server Manager or ArcGIS Pro

Description

After a Server Object Extension (SOE) or Server Object Interceptor (SOI) is deployed to ArcGIS Server, the option to enable the SOE or SOI in ArcGIS Server Manager or ArcGIS Pro only shows up for services published from ArcMap, but not for services published from ArcGIS Pro.

Cause

This is by design. The behavior happens because the SOE or SOI is built for services published from ArcMap instead of services published from ArcGIS Pro. The SOEs and SOIs built with the ArcObjects SDK for .NET or Java only work with services published from ArcMap. Starting with 10.6.1, services published from ArcGIS Pro support SOEs and SOIs built with the ArcGIS Enterprise SDK.

Solution or Workaround

To allow an SOE or SOI to be enabled with services published from ArcGIS Pro, the following prerequisites must be met:

1. The service is published from ArcGIS Pro 2.2 or later version.
2. The service is published to ArcGIS Server 10.6.1 or later version.
3. The SOE or SOI must be built using the ArcGIS Enterprise SDK instead of the ArcObjects SDK. 

If you have an existing SOE or SOI built with the ArcObjects SDK, you should follow the Migration Guide for .NET or Java to migrate the project to be built with the ArcGIS Enterprise SDK. 

Note: 
This process requires development efforts. If you are not the developer of the SOE or SOI, you need to contact the SOE or SOI developers to make this change. After the SOE or SOI is built with the ArcGIS Enterprise SDK, it can be deployed to ArcGIS Server (10.6.1 or later version) and enabled with services published from ArcGIS Pro (2.2 or later version).

You can also find out if an SOE or SOI is built for services published from ArcMap or ArcGIS Pro by visiting ArcGIS Server Manager > GIS Server > Extensions page to check if the extension’s Provider is ArcMap or ArcGIS Pro, as shown in the following screenshot.

• The SOE or SOI built with ArcObjects (with ArcMap as the Provider) can only be enabled with services published from ArcMap.
• The SOE or SOI built with the ArcGIS Enterprise SDK (with ArcGIS Pro as the Provider) can only be enabled with services published from ArcGIS Pro.

If you need the SOE or SOI for both services, you should compile separate SOE or SOI projects using each SDK and deploy both .soe files to the server. 
Read more about the differences between ArcGIS Enterprise SDK and ArcObjects SDK.