I have created a sample project - GitHub - vivekanand-mishra/app-insights  Checkout and deploy in your local and follow the testing instruction on Github page.

Anyone looking for a direction to similar issue can find this link useful to solve this- Experiencing Adobe Experience Manager - Day CQ: AEM 64 - Extend TouchUI Rich Text Editor Table Plugin, Add Summary Field

We have done a small POC with App Insight successfully. But our use case was to track request and send analytics to App Insight.  Before I suggest something, I need more info to understand where problem might be-1. Do you see the applicationinsights-web dependency resolved in your core project? You ...

Reported the issue to Day Care, Hope it gets resolved soon. Meantime you can have some workaround in your local. Try this- Re: Adobe Public Repository (https://repo.adobe.com/nexus/content/groups/public) is not accessible