An update to Azure Automation has just been released. A node that's managed through Operations Management Suite can now be used as a Hybrid Runbook Worker and can be onboarded to Update Management at the same time. You need to use the same Automation account for both.
You can verify that the latest version has been applied to your Microsoft Monitoring Agent by confirming that the following subfolder matches this version number: %ProgramFiles%\Microsoft Monitoring Agent\Agent\AzureAutomation\7.2.12024.0.