Hi David Vanden Bussche Thanks for reaching out. Could you please confirm if your APIM instance is in VNET? Use the portal to check the connectivity of your APIM instance to dependencies, such as Application insights.
In the portal, in the left-hand menu, under Deployment and infrastructure, select Network > Network status.
If the status is in failed state, make Sure that outbound connectivity to the telemetry endpoint is allowed from the VNet.
please verify if the NSG for your APIM subnet has been configured as per this document.
Feel free to reach out if any questions, I would be happy to assist you.