My two cents
In my free course, "What is Service Design?" I summarise what a service designer does in these four activities:
Research: Understand what people want or need
Sense-Making: Summarize what they have learned
Ideation: Come up with 100 new fancy solutions
Prototyping and testing: Build new solutions for testing and help implement them once they are tested
Outside of these specific service design tasks, service designers also have to do the usual tasks that any other knowledge worker does, like, for example do project management, share their ideas and onboard others to understand them better.