What you need to do at each layer of management:
What is it like being a manager? The answer to that is really different depending on what level of management you are operating at. Its well understood that being an IC is much different than being a manager (I've written about this a few places, most recently in Owning Decisions), but its also true that each level of management is very distinct and what will make you excel at one level may not be enough at the next level.
There are a number of things that change as you move up, but the one I want to highlight here is your relationship with the people you directly manage. Here is a simple way to look at it:
Manager of ICs: You are a coach for those doing the job. You should really know how to do the job and be able to step in and be very good at the job. People you manage expect you to be able to teach them how to be facets of their job better.
Manage of Managers: You are a coach for Managers! No longer do you worry about tactically achieving an outcome, but rather how can the managers you manage do a good job at managing! Super different, and to a certain degree, is a more translatable skills (Coaching managers is more generic than coaching engineers or customer success, which requires specific knowledge). Being able to do a great job at the underlying core work is less important (for instance, a Engineering Manager of Managers may be only a subpar engineer but still be very effective in their role, while an Engineering Manager of ICs will likely need to be excellent at engineering itself).
C-Level: Great at hiring managers. The CEO, for instance, has to do a lot of things. Being a good manager is actually not a requirement in my opinion, but they MUST be great at hiring great managers.
Each level may encompass the previous levels (like its a good thing if your CEO is also a great manager of managers) but the skills needed in lower levels of management are no longer determinant of success at the current level.
As you move up, pause and reflect on what you like about your job and whether the next rung gets you closer or further away from what you excel at and love doing. If you want to make the next leap, work on the skills that will be valuable in the next role.
I hope this helps.