They do for sleep. This is taken from their site:
"While you’re sleeping, your device tracks the beat-to-beat changes in your heart rate, known as heart rate variability (HRV), which fluctuate as you transition between light sleep, deep sleep, and REM sleep stages. When you sync your device in the morning, we use your movement and heart rate patterns to estimate your sleep cycles from the previous night."
Now if you are looking to actually see your HRV then you would need something like a new polar device. You can actually see your HRV numbers right in the app and on the watch. With the Garmin's, they can do HRV as well using their body battery and stress widgets but don't show your actual HRV numbers like Polar does.
Hopefully this helps.
