tests: move doc tests to the unit test stage

- Frequently, the documentation build will fail mysteriously in some
  spack command.

- The cause is some new bug introduced by the PR, but this is not
  apparent because the unit tests haven't run and the doc tests aren't
  targeted at code bugs.

- Users end up puzzled by doc failures when they're really code failures.

- Move the doc tests parallel with the code tests, so that we can more
  easily see bugs like this.