I am currently in my second year of a PhD program. I have not yet decided on academia, industry, or entrepreneurship for a career, but in all these cases my success will be strongly influenced by my ability to lead and manage a team of students/postdocs, research engineers/technicians, or co-founders/employees.
I have found that graduate school offers no opportunity for practicing the kinds of interpersonal skills most relevant to leadership (delegating tasks, maintaining motivation, creating an inclusive atmosphere, resolving conflicts, etc.). Note that I distinguish leadership from teaching and mentoring. The closest thing I can think of would be to mentor an undergrad in research. The situation will likely be similar if I do a postdoc.
How can I practice or develop these skills while still in graduate school? Or what would be some important surrogate skills I should focus on instead?