Cancel `Internal Tests` private job if the public job is cancelled

When a public `Internal Tests` job is cancelled, cancel the corresponding private job as well.

# TODO
- Split the job into a part that kicks off the workflow, and one that waits for it
- Do something like this to cancel the job that was kicked off:
```
  - name: Run only if job was cancelled
    if: ${{ cancelled() }}
    run: echo "Job was cancelled!"
```