Support for managed connectors is currently in preview and still, the product team is working on supporting ‘Azure Monitor Logs’ with service identity and it might take some more time.
For now, we will remove Azure Monitor Logs from the supported connectors list: from the list of supported connectors here https://learn.microsoft.com/en-us/azure/logic-apps/create-managed-service-identity
Once it is tested and fully supported we will be updating our documents