Automate unit and regression tests with GitHub actions?

[brendanreardon]

After the recent Pull Request ensuring compatibility with Python 3.13, I looked into ways that we can run unit tests and regression tests for both Python 3.12 and Python 3.13 without needing to manually run them all ourselves. Looking around, it seems like people do this with GitHub actions.

At minimum, we would want to have the GitHub actions make sure that no warnings or errors are produced and (i) run the unit tests and (ii) run the regression tests. We may need to modify how the regression tests are run, perhaps caching the expected (or "pre") outputs on GitHub. We can perhaps have this exist in the example_outputs/ folder and keep that up to date, rather than have additional outputs elsewhere.