I'm looking for a privacy-respecting solution for a smartwatch as well. I actually think privacy is even more important on a smartwatch than a phone.
I currently have a Galaxy Watch that I modded to unlock extra features, but I'm still trying to get it set up to sync to my phone. Samsung's requirements for that are absurd. You have to jump through a bunch of hoops if you want to use a non-Samsung device. You have to create a Samsung account, and they try to ban temp emails and get you to use a phone number for 2FA. They force you to use a phone number when setting up their Health app. It needs to be on the owner profile. It needs access to your phone records and contacts, access to nearby devices, etc. The hardening process has been enough work I'm considering just giving up and switching to something else.
If I were to guess, Garmin would be the least onerous when it comes to privacy issues? I don't really know much about Amazfit, though.