Makes sure the thing holds together under every load it will see.

Structures work is the discipline of load paths and margins. You take a set of load cases, work out what the structure does under each one, and either prove it survives or change it until it does, usually while someone is asking you to remove mass.
The standard route, and the one most employers list.
Increasingly common: paid work from day one with the degree alongside it.
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.
The work is meticulous, repetitive in places, and unforgiving of small errors, because the small error is the one that gets through review. Much of it is justifying a design that already exists rather than creating one.