Let’s go off on a topic near and dear to my heart: you need to stop qualifying your team leadership as having been "just with students" or "just part-time student employees" or anything else that implies that it's dishonest to describe the work you do supervising and managing a team of part-time student employees as "managing a team".
There are a couple reasons I feel really strongly about this! It does a disservice both to them as people and to you as a competitive candidate. Everyone here deserves better!
The master's degree that allowed me to practice HESA work was a master's degree in College Student Counseling, which described itself early on in the program as applying the intersection between an activity (counseling) and a setting (college campuses) to a certain group of humans (college students). I think this is why I've always pushed back against the idea that there is something about traditionally-aged college students that make their development incomparable to any other 18-24-year-old person. I also think this can be a key realization to generalizing our experiences working with them as we pivot into industry or corporate.
Traditional-aged college students go through the exact same human development processes as a person who doesn't go to college immediately after high-school, and then there are also a few contextual development processes that are layered on top of this that they receive from their collegiate environment. (Many of these, e.g. leadership experiences, support outcomes can also be gained from life outside college.) Ideally, we support these students in ways that are nuanced, and tailored to their development, but I assure you: 18-24-year-old college students do not develop as people by virtue of being college students. For even the most involved student, "college student" is a partial (and temporary) identity.
My experience is that as student affairs professionals, we excel at recognizing the contexts where students are just humans who happen to be going to school. I want us to be able to do this when we're talking to folks outside higher ed about the work we did. Because...
Once you understand how to operationalize the processes that go into team management, it becomes clearer that there is no need to say "I led a team of people (but they were part-time students working 15 hours a week)." When a person describes having led a team, here's what they're saying:
What on that list becomes less of a full-time job because a person is a college student, or because they work part-time?
Lots of folks in corporate lead teams of part-time employees, or employees who are still in that 18-24 age range. I can assure you that folks leading part-time employees at Amazon do not represent this leadership position on their resume by saying "led a team of part-time employees".
Did your students have to fill out a Student I-9 to begin working in your office? Did you issue them a Student W-2 to summarize the work they did for you during the year? Did you pay them in Student dollars?
The answers to all of these questions are no because these students were real people performing real labor at real jobs and you were their real manager. You get to claim that. You get to say that you supervised a team of employees. You do not have to say that you supervised a team of part-time student employees.
Some of this I think is rooted in semantics. We refer to full-time masters-level employees as professional staff members, which implicitly frames undergraduate student employees as the opposite of "professional staff members". I think this can unconsciously lead us to devalue the work that they do (or the work that we do in managing them).
I also think there's a stigma that "part-time" work is less impactful or less "real" than full-time work. But another way to frame this (for ideal cases, I recognize) is that we've allocated student resources appropriately given the scopes of the projects to which they contribute. A project with a small-to-medium scope is still a complete project.