Are you trying to write back the password to the on-premises Active Directory? The on-premises writeback feature requires Azure AD Premium P1, Premium P2, or Microsoft 365 Business Premium, and it sounds like that might be why this stopped working after the license change. Otherwise if you are using cloud-only SSPR, the plan you have is enough.
Password reset errors
While accessing the password reset portal, users are receiving the following error:
ACTIVITY TYPE: Change password (self-service)
STATUS REASON: ADAdminActionRequired
We have recently moved from an E3, Azure AD P1 license to an M365 E5 license.
Any reason why this would quit working after a license change?