CMIIW, but isn't the Stylist career for active sims while the Stylist role is for inactives that got assigned to a styling station?

the role is meant for service NPC, homeless Sims. If you enabled in Register that residents can be assigned, only then this can happen, but it is not the career.

inactive residents are the ones who live in houses of town. You can assign the stylist career via MC, but they won't get auto assigned.