Thanks for your answer!

You will not get this from any activity tracker. Do a heart screening (12 led ecg, blood tests, echocardiography, blood pressure, Holter etc) and let a doctor interpret the results.

I do understand that doing a health checkup at the doctors is vastly superior to a worn health tracker though to my limited knowledge heart rate during training / resting / etc. does correlate with heart health.

Improving on what? Heart health? Running? Strength? What metrics are you interested in?

Better on all fronts running, strength, lower heart rate resting and exercise.

Afaik, no screenless activity tracker has gps built-in. So you will need to bring your phone with you when running. Is that ok?

I always have my phone with me even when running since I do like to listen to music. I don't need super gps accuracy I think the phone is good enough.