Thank you for reaching out to the Microsoft Q&A platform.
I can suggest you some steps on high level here along with relevant document links to support you.
To use an Entra-only user account in a scheduled task on an Entra-joined VM, you can create a user-assigned managed identity for your Azure Automation account and use it to access other resources, such as your SQL Managed Instance.
https://learn.microsoft.com/en-us/azure/automation/add-user-assigned-identity
Create a PowerShell runbook in your Azure Automation account that authenticates to your SQL Managed Instance using the user-assigned managed identity. https://learn.microsoft.com/en-us/azure/automation/learn/powershell-runbook-managed-identity
Create a scheduled job in your Azure Automation account that runs the PowerShell runbook at the desired frequency
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