I don't think we should use the group concept for managing permissions in admin endpoints. That'll just be to confusing IMO. In either case we don't need a distinction between user and client, as we'd have roles for that.
What about domain/organization or something? Within a realm you could have one or more organizations. Users and clients belong to a single organization. Then we'd have a role namespace for the organiztion for example roles would be:
* org.keycloak/<organization name>/view-clients
* org.keycloak/<organization name>/manage-clients
* org.keycloak/<organization name>/view-users
* org.keycloak/<organization name>/manage-users
In fact you don't need groups to do that, just role namespaces and the ability to configure what "namespace" is used for a particular client or user.