Owns how the whole spacecraft fits together, not any one part of it.

Systems engineering is the discipline of the interfaces. Power, thermal, propulsion, comms, attitude control and payload each have specialists; the systems engineer owns the budgets they all draw on, the requirements they all trace to, and the failure modes that only appear where two subsystems meet. Most of the job is asking hard questions early, because there is no maintenance visit afterwards.
The usual route. Spend a few years deep in power or thermal, then move outward.
A direct route, and stronger when it follows some hands-on experience.
Aerospace engineers · US Bureau of Labor Statistics, Occupational Outlook Handbook, May 2024 wages and 2024–34 projections.
Counted inside "aerospace engineers", along with every other engineering discipline that works on air and space vehicles. There is no separate published line for this specialism.
You are responsible for everything and expert in nothing, which is uncomfortable for a long time. There is no maintenance visit after launch, so a question you did not ask early becomes a mission you cannot fix. Reviews are where careful work meets six specialists who all want something different.