We've had two BFs recently that are difficult to investigate because add_remove_shards.py has its own timeout mechanism that causes it to fail gracefully instead of timing out in evergreen. This prevents the hang analyzer from being invoked automatically.

We got lucky in BF-40097 that the same issue was independently discovered in a separate test, so we put off doing this. However, we now have BF-41719, which is proving similarly difficult to investigate. We should explicitly invoke hang analyzer during a timeout in the hook.