Hybrid and on-prem AD
Set up a hybrid worker with a PowerShell runbook so ServiceChanger also fills on-prem AD groups, with write-back through Entra Connect.
The idea
ServiceChanger writes cloud-only groups directly through Microsoft Graph. But groups that sync from on-prem AD into Entra are read-only in Entra: Microsoft does not allow membership writes on an on-prem mastered group. So the change has to happen on-prem.
For that, a PowerShell runbook runs on a hybrid worker alongside your cloud connection. That is a Windows host in your own network that can reach your domain controllers. The runbook applies the group memberships in AD. Your existing Entra Connect then syncs that change back to Entra, so the cloud picture matches.