Deep breathing activates the parasympathetic nervous system which decreases the heart rate and dilates blood vessels, reducing your overall blood pressure.

Strengthening the muscles you use to breathe make it easier to do and thus puts your body in a relaxed state more often.

You don't need a device to do this. You can also do any popular deep breathing exercise like Wim Hof, square breathing, 4/7/8 breathing, or restricting airflow with thumbs in nostrils. A device may be more effective at training your resistance however.

Additionally to the parasympathetic changes, there are mechanical effects. the lungs are a negative pressure system. When you breathe, you drop the diaphragm, increasing the negative pressure in your chest while also increasing the positive pressure in your abdomen. Blood flows through the vena cava (the main vein bringing blood back to the heart which runs through the abdomen and chest) towards the negative pressure. This means more blood gets back to the heart (“increased preload”) and so the right heart can pump more blood to the lungs, and more blood gets to the left heart to be sent around the body without the heart muscle actually having to do more work.

Thank you! This is exactly the answer I was looking for!

As well as strengthening your breathing muscles (there are very many I guess) restringing air flow on an in breath, like in Ujjayi Breathing, brings more blood into the alveoli because of the low pressure in the lungs. I guess this would have some effect like enhanced gas exchange.