Senior TPMs execute programs well. Staff TPMs define what programs should exist. That is the simplest version of the difference, and it understates how different the day-to-day actually is.
At the senior level, you receive scope. The program is defined, the stakeholders are named, and your job is to drive it to completion. You are excellent at this. The promotion to staff is not a reward for being excellent at it. It is a signal that the organization believes you can do something different.
What staff requires is the ability to look at an organization's work and identify the program that is missing. Not the program that someone asked for, the program that the business needs but has not yet articulated. That requires understanding the business deeply enough to have opinions about where the risk is, what the next constraint will be, and what needs to be built before the build that everyone is already planning.
The other thing staff requires is a different relationship to ambiguity. Senior TPMs work in ambiguous situations. Staff TPMs are comfortable being the person who makes them less ambiguous for others. That is a leadership posture, not a project management skill. It means writing the framing document before anyone asked for one, running the alignment meeting that nobody scheduled, and making the decision that was waiting for someone to make it.
The path is specific. Find the program your organization needs but has not named. Name it, scope it, and drive it without being asked to. Do that once and it is an accomplishment. Do it repeatedly and it is a pattern. That pattern is what gets you to staff.