Thanks for the question and using MS Q&A platform.
It seems that the issue you are facing is related to the fact that the Azure SSIS IR still creates two SQL accounts (AzureIntegrationServiceDbo and AzureIntegrationServiceWorker) that are used to run the SSIS IR, even when Entra ID Auth Only is enabled on the Azure SQL DB.
As per the official statement from Microsoft that you mentioned, Entra authentication with the specified system/user-assigned managed identity for your ADF is only used in the provisioning and subsequent starting operations of your Azure-SSIS IR that will in turn provision and or connect to SSISDB. For SSIS package executions, your Azure-SSIS IR will still connect to SSISDB to fetch packages using SQL authentication with fully managed accounts (AzureIntegrationServiceDbo and AzureIntegrationServiceWorker) that are created during SSISDB provisioning.
One possible workaround for this issue is to create a SQL Server login for each of the fully managed accounts (AzureIntegrationServiceDbo and AzureIntegrationServiceWorker) and grant them the necessary permissions to access the required databases. Then, you can use these SQL Server logins to connect to the databases instead of using Entra ID Auth Only.
Alternatively, you can consider using Azure Key Vault to store the credentials for the fully managed accounts (AzureIntegrationServiceDbo and AzureIntegrationServiceWorker) and retrieve them at runtime in your SSIS packages. This way, you can avoid storing the credentials in plain text in your SSIS packages and still use Entra ID Auth Only.
I hope this helps. Let me know if you have any further questions.