Self Service Password Reset with on-premises writeback in Microsoft 365 Business

That is correct. Office 365 E3 does not have SSPR for hybrid accounts. This was only available in Azure AD Premium until very recently, when it was released into Microsoft 365 Business. M365B has always been a strange beast—more than Azure AD that is included with Office 365 but it is also not quite the full AAD P1 either. Stands alone as something unique and in between. Azure AD Plus maybe. Personally, i don’t understand why they didn’t just make this subscription a couple more dollars and include the full EMS E3 SKU with AAD P1, especially for Conditional access. If I had it to pick any of the P1 features I would prioritize that one alone. On-prem/hybrid is going to be dead in another year or two anyways in the small business, so who cares about pw write back? Join your PC’s to Azure AD, and go cloud only accounts. On prem can fade into legacy—there to support an app maybe, like Quickbooks and nothing more.