@Marko Žlogar Kindly note Application Insights currents supports a list of dependency calls automatically without any modification to your code. For currently supported list of dependency calls, refer this document.
As Klaviyo API is not in the list of supported dependency calls, you need to track it using TrackDependency call. This document provides sample examples on how to track dependency calls manually.
Kindly go through the reference documents and make changes to your application accordingly.