melgaard.nu 
I am working intensively with Application Insights (I want to see and act on errors before my users do!), and when I write plug-ins, I like to export custom telemetry to Dataverse. You can read more about it in the Microsoft Learn article.
Also see this excellent blog post
One interesting issue I had with one of my newly created environments was that it refused to export custom telemetry. It exported everything else. I tried to create new exports, pointing at other Application Insights instances, nothing worked!
It turns out that the telemetry key in this environment was not set correctly for some odd reason. So, the solution was to set it manually by patching it on the Dataverse instances organization record.
It’s relatively straightforward.
Find the instrumentation key for the Application Insights instance you want to export to
Find the GUID of the Organization from the Power Platform Admin Center
Update the column “telemeetryinstrumentationkey” for the “organization” record of the Dataverse environment, to the instrumentation key of the Application Insights instance. And for good luck sake, set the “orginsightsenabled” to true.
Notice that the “telemeetryinstrumentationkey” will appear as null if you lookup the record.
You can see how to do it easily from the browser here:
You should now see your custom telemetry being exported to Application Insights.