Sure John, it is totally feasible; let me explain in broad strokes:
You can create an Azure Function in PowerShell with a trigger timer (for the time or cron you prefer) and enable its System-Assigned Managed Identity. Then, in Azure AD assign the necessary Graph roles (User.Read.All, Group.Read.All, GroupMember.ReadWrite.All, Directory.Read.All, and Sites.Read.All) and the Exchange Administrator role for ExchangeOnlineManagement to this identity as “Application permission.”
In your run.ps1 replace the Connect-MgGraph -Scopes and Connect-ExchangeOnline with the -ManagedIdentity versions. At this point, when Function starts (manually or via timer), it authenticates itself and can read the SharePoint list, query Graph, and manage groups without any interaction.
Do a first manual test, take a look at the logs, and you're up and running in unattended mode