My two cents
Service Design complements UX well. To me there are two main benefits of learning Service Design for someone who's already working as a UX designer:
Service Design will make you consider the backstage
You'll learn how to create experiences and services that are not only lovely for the end user but that are also lovely for the people who have to manage them in the behind the scenes. That's where tools like the Service Blueprint will be a great addition to your toolbox.
Service Design will make you work outside of the digital experiences
Most services aren't purely digital or physical. They are a mix of many different experiences (in-person, phone, web, paper, etc). Service Design will teach you to think about the mix of all these elements to create one complete experience.