I use a Garmin Vivosmart 4 or a Xiaomi Mi Band (v4 or v5) and simply don't connect it to the smartphone. That gets you access to the data on your wrist, but no log of the data. Great privacy with no data collection. If you want data collection maybe you can find an app that doesn't upload to the cloud or write your own; some fitness tracking apps can talk to a variety of devices and don't use the cloud. The Gadget Bridge web site has a list of which devices are compatible with it:
* Empatica E4 (required to adhere to GDPR) (for more advanced use)
* Microsoft Band 2 (open source API on Github)
* Suunto (required to adhere to GDPR)
Personally, the Garmin Fenix 6 or Garmin Enduro (if the new Enduro gets good reviews) are the ones I would recommend for general use.
Apple may do various appealing things, but they are not obligated to adhere to GDPR. The app creators for the Apple Watch are certainly not required to adhere to GDPR.
Ironically, the ones that adhere to strict privacy regulations tend to have more solid technology. These technologies have been utilized for impressive research in journal articles.
https://github.com/Freeyourgadget/Gadgetbridge
They do list the Pebble Steel. I'd try the Mi Band 5. The Vivosmart 4 is somewhat unstable in my experience.