An Azure machine learning service for building and deploying models.
With Allow only approved outbound, the AML managed network can create private endpoints only to supported targets. Microsoft's current list includes Azure SQL Server, not Azure SQL Managed Instance. A direct managed private endpoint to SQL MI is unsupported; the AzureMachineLearning service tag permits traffic but does not create private routing.
Use AML compute in a customer-managed VNet. Peer it with the SQL MI VNet, or create a SQL MI private endpoint in a VNet reachable from the compute. Configure DNS so the exact SQL MI hostname resolves to the private-endpoint address, use that hostname in the connection string, and permit TCP 1433. Test DNS and TCP connectivity from the compute node.
Managed virtual networking cannot be disabled on an existing workspace, so this design may require a new workspace. Do not use an FQDN outbound rule as a workaround; AML FQDN rules support only ports 80 and 443.