The BEST description of the guidance provided by Service Design is?

This is too narrow; Service Design explicitly covers improvements to existing services and the design of service management processes, not only new services.

This is also incomplete; Service Design addresses new services, not only improvements, and it always includes the design of supporting service management processes.

ITIL Service Design provides guidance on designing new and changed services as well as the service management processes, tools, technologies, and measurement systems required to deliver and manage those services. This holistic scope - captured in the 'Five Aspects of Service Design' - ensures that supporting processes such as capacity management, availability management, and continuity management are designed alongside the service itself.

Day-to-day operation and support of services is the scope of ITIL Service Operation, which covers event, incident, problem, access, and request management.