Where I work scrum masters are supposed to “help teams improve”. That’s measured, in one way, by looking at the current rate of performance of a team and projecting it out. Then a scrum master needs to improve the team’s performance by some amount that exceeds the cost of having them there.

Some examples, number of on time deployments, number of story points, number of bugs... I’m not saying this is perfect, but that’s how some people are measuring.

So if a PE is responsible for improving juniors, I suppose a PE can be judged on the size and complexity of projects their juniors are able to take on. Maybe the time to promotion and number of juniors getting promoted?

Unfortunately, it tends to be a bit "squishy" - task completion (by the PE or by junior team members), team velocity, etc can all be used, but using them exclusively is just asking for the team to game those metrics. Much better to have regular 1-on-1s with each person and just discuss progress - team progress, individual project/task progress, and any career goals. If somebody is actively seeking promotion, we'll use a job progression matrix (HR puts them together) and talk through the differentiators and what that employee can do to fill the gaps.