Vague question, as privacy means different things to different people, but its very hackable, so as long as you're running Android you should be able to make it work how you want.
By default it uses the Pebble App for sync. You can decide whether that meets your privacy needs or you want a custom app. Someone has probably shared how to do what you want.
See the other trending HN post for Apple compatibility (TL;DR it sucks because Apple makes it suck).
Thanks. Sorry if it was vague. Basically my first preference would be to not have any need to connect to a mobile phone (so no android or apple). And if that is not possible it is preferable to connect via de-googled Android. I guess I need to find out whether Pebble App sync works on GrapheneOS, and whether Pebble App sync requires internet/data permission - just trying to make sure the data doesn't leave my phone.
You need a mobile phone since they don't have internet access directly.
After that you should be totally fine, what are you hoping for your smartwatch to do? I primarily use my pebble for notifications from my phone to show up on my watch which doesn't require any sort of external access.
I need it to track my heart rate. I am actually also looking forward to something that can track my blood-pressure, but I am not sure whether the technology is there yet. A device that can do offline tracking would be ideal, ability to sync with a USB cable would be icing on the cake.
By default it uses the Pebble App for sync. You can decide whether that meets your privacy needs or you want a custom app. Someone has probably shared how to do what you want.
See the other trending HN post for Apple compatibility (TL;DR it sucks because Apple makes it suck).