ci: Add basic clang-tidy check to linter workflow

ci: Add basic clang-tidy check to linter workflow

Let's add a basic clang-tidy check to the linter workflow. This
gives us the following:
- A check so that we don't introduce any new cyclic header dependencies
- A check to make sure all of our header files are standalone, as clang-tidy
  will fail to parse header files that don't include all their dependencies.