As of today, there are no attribute stores in AAD.
If synchronizing from On-premises is not an option for you, then I would recommend Azure AD directory schema extension attributes which provides a way to store additional data in Azure Active Directory on user objects and other directory objects such as groups, tenant details, service principals. Only extension attributes on user objects can be used for emitting claims to applications.
Directory schema extension attributes are always associated with an application in the tenant. To learn more about : https://learn.microsoft.com/en-us/azure/active-directory/develop/active-directory-schema-extensions
Hope this helps.
Regards,
Siva