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stage manager is a leader of people. Every leader has their own style to how they organize the work getting done and their own way of keeping it under control. In addition to the organizational and relyance skills when under your control, you must look deep into your self as to how and why you were trusted as this leader in keeping to your personal style of leadership and to the most adventagous method of extending that same leadership role you have already asserted into a more broad way of getting the job done on a larger aspect of it.
In other words, organize as you will, note what needs to be done both within your ability to supervise properly and not, but a good leader of people does not need to organize and specialize as much as communicate what they need to be done and by whome.
This especially becomes tricky if only a good tech person but not a leader of a crew. Still rely upon your style and what is most fair in balance with what's necessary to get the job done.
In addition to organizational skills to a lesser extent, I say a stage manager is a good leader of people by way of their own style for doing so. Work and emphisize on this and you will lead.