“How does dental health relate to heart health?”

Most definitely. Some studies are showing gum disease may play as a factor in Alzheimer’s

There is definitely an association between poor dental health and gingivitis (gum disease) and atherosclerosis or hardening of the arteries that affect the heart arteries and cause heart attacks. The cause and effect of this is not as clear. It may be that people with poor dental health also have higher risk factors from bad eating habits or high blood pressure or diabetes. However, there may be a separate inflammatory component that accelerates vascular disease when you have poor dental health.

Many of the bacteria found in periodontal (gum) disease have been found to cause problems with your heart valves. Here's an article you can read for more details.
https://www.health.harvard.edu/diseases-and-conditions/gum-disease-and-the-connection-to-heart-disease