How might a Scrum Master’s responsibilities change once a team has some experience with Agile methodologies?

There's always room for improvement, even with a mature team and this is where the Scrum Master can help. For the most part my team is self sufficient and are familiar with Scrum and other Agile frameworks, but they still fall into bad habits and we're always looking for ways to constantly improve (development, performance, team dynamic, etc.). A great SM always has their eye out for new techniques or tools that they can bring back to their teams to explore. Aside from helping my team, I also help enterprise wide to mentor and coach new teams in the org and working with leadership to adopt this way of working (our company is bimodal).