This feature depends on the Analyze model-driven apps and Microsoft Dataverse telemetry with Application Insights feature.

The instructions describe how to enable exporting data to Application Insights. See Export data to Application Insights

Step 6 says:

Select the Azure subscription, resource group, and Application Insights environment that you're exporting data to. Select Next.

You must have contributor, writer, or admin rights to the Application Insights environment. Typically, one production environment or tenant maps to one Application Insights environment.

You should verify this is set up correctly and that you have the appropriate rights to the Application Insights environment.

You should not have to set the organization.telemetryinstrumentationkey column. That column is valid for update but not valid for read. It should never return the key value. This is by design. But it makes it hard to verify whether the key value is stored.