Can I create a rule that only notifies me, without pausing campaigns or changing the budget?

To get notifications only, use the Alerts page: create a New Alert with the metric and threshold you want, and you'll be notified without anything changing in your campaigns. Automated Rules always perform one of the actions available in the form (Pause, Activate or budget changes). A common approach is to use both together: an alert with a looser threshold so you find out early, and a rule with a stricter threshold to act automatically if things get worse. That way you stay in control and still have a safety net.