Slow breathing (in yoga: pranayama) instantly down-regulates your nervous system by boosting vagal tone and lowering sympathetic "fight-or-flight" activity. When your breath lengthens, it signals your brain that you are completely safe, dropping your heart rate and lowering blood pressure.
It doesn’t signal anything. Your heart rate drops because you’re inhaling less oxygen so your heart is like “we don’t need this high fi flow” and slows down blood flow to lower energy expenditure.
Lower energy state always wins unless chasing energy source.