Add github action to test tools

[dakom]

See #154 (review)

[JakeHartnell]

Done.

[ethanfrey]

@JakeHartnell If you close issues, can you link a PR or some code to justify it?

I am seeing a number I think are incorreclty closed.
And if you look at github actions and the Carog.toml exclude line you see it is not tested.

That said, the requirement was mainly about climb stuff, so maybe a link to CI tests covering those tooling in those repos would be good to close this. Otherwise, it should be moved to those repos.

There was a good intention behind the issue and maybe repos moved faster than the issue, but don't just close