what are the kinds of tests do people write in other areas of the industry?

Aerospace here. Roughly this would be typical:

- comprehensive requirements on the software behavior, with tests to verify those requirements. Tests are automated as much as possible (e.g., scripts rather than manual testing)

- tests are generally run first in a test suite in a completely virtual software environment

- structural coverage analysis (depending on level of criticality) to show that all code in the subsystem was executed by the testing (or adequately explain why the testing can't hit that code)

- then once that passes, run the same tests in a hardware lab environment, testing the software as it runs on the the actual physical component that will be installed on the plane

- then test that actually on a plane, through a series of flight tests. (The flight testing would likely not be as entirely comprehensive as the previous steps)

A full round of testing is very time-consuming and expensive, and as much as possible should be caught and fixed in the virtual software tests before it even gets to the hardware lab, much less to the plane.