I think you used the word leadership just fine. In most professional settings, leadership is a de facto title for those in management roles. Unfortunately most management roles go to people with experience in the company not leadership in the company necessarily. You seem to be playing on the spectrum of servant leadership where people know you are capable, you are liked and given opportunities to shine. What you need to do is become limited. If possible refrain from always saying yes, ask for certain deliverables and based on that decide if you want to say yes or no. If something is too time consuming I would say no if i have other work at hand. Work with others if you do take a responsibility and ask for help even if you don't need it. As you get others to help you find ways to share insights with others so that little by little you become an expert contributor in your office thus growing in value.

The thing about leadership is that people don't know what it means. When I interview, i ask, those who say they want to be leaders in our organization, what do you mean? Most don't have a clue. Leadership is like gravity, we use it to explain why an apple falls to the ground is just what we call it..it doesnt explain the mechanics, the why or how...

When you think of leadership don't think of it as the all supreme magical authority of everything. Focus on a niche, what are you good at, what does the department need help in? You can be a leader in a project or a leader in mathematics in a school or a group.

See it this way:
Leadership in _______ = Expert known for and trusted in _________ (this is the path to management in or out that company)

Truth be told is that we always think we deserve that one up job, we deserve more pay, etc. Sometimes is true sometimes is not, but the fact that you want to move up the ladder is all that you need. If you see no potential for growth take your skillsets to another company.