You can deploy server object extension (SOE) developed with 11.2 version of ArcGIS Enterprise SDK into ArcGIS Enterprise environment configured in Kubernetes environment. Java development environment and steps for creating SOE using ArcGIS Enterprise SDK are same irrespective of which ArcGIS Enterprise environment (Window/Linux and Kubernetes) you targeting to deploy it.
In Kubernetes environment, map service based SOEs are supported only. Plus, SOE can only be enabled while publishing service from ArcGIS Pro. As of now server object interceptors (SOI) developed using 11.2 version of ArcGIS Enterprise SDK are not supported in Kubernetes environment.
Follow the steps below to deploy SOE in ArcGIS Enterprise environment deployed in Kubernetes environment and enable it on map service.