What is the ratio of breathing rate to heart rate?
"This is because the heart is connected to the lungs via the pulmonary artery." It's not like heart rate or breathing rate are regulated by pulmonary arteries. The relation is more sophisticated than that. For example heart rate is controlled by nerves and hormones, and neither comes straight from the lung. But fast breathing leads to changes in blood oxygen and pH, which are picked up by sensors such as the carotid body, which informs the medulla, which then talks to the sinoatrial node. There is also more direct influence, because ample breathing increases pressure in the thorax.

But at each step, there are many other factors interfering, meaning the correlation between the two gets ever looser. There isn't really a "normal" ratio of heart rate to respiration rate. There is a healthy heart rate and a healthy respiratory rate, but they are both wide intervals (60-100 and 12-20, respectively). Dividing one by the other, you get a very wide interval, from 60 beats per minute / 20 breaths per minute = 3, to 100 beats per minute / 12 breaths per minute = 8.

Perhaps in practice the most common values for beats per breath are in a narrower interval. But "normal" values are defined in relationship to abnormal conditions, and there is no disease in which a change in this ratio is a cardinal feature. It makes little sense for clinicians to define a normal range for beats per breath, and therefore it makes little sense for epidemiologists to estimate most common values.