When configuring this on my home tenant, I received the following error:
All usual suspects were covered: the correct licenses were assigned, password writeback was configured and showed up in the portal as working, so no issues there. When opening the SSPR section in the Azure Portal, the following error was shown:
Digging into the Event Viewer on the Azure AD Connect Server revealed the error: The password could not be updated because the management agent credentials were denied access.
Following best practices from Microsoft, the account that was configured in the Azure AD Connect management agent did not have elevated permissions, and therefore did not have the possiblity to reset passwords.
Assigning delegated permissions to reset the password of the OU containing the synced users, solved the issue.