I use a Xiaomi Smart Band 7 and pair it with Gadgetbridge, and it works fine for my purposes, which is HR-monitoring during the day, sleep and workout sessions. I rarely interface with the watch itself (which is by design), so if you want more functionality out of your watch, then this might be a little on the light side feature wise. I tend to keep Bluetooth off, so I connect to it maybe once a day to sync data with Gadgetbridge, which I again export for analysis. A bit clunky to connect - I have to search for it first in the Gadgetbridge app, and only when it has found it can I attempt to reconnect. Maybe this is easily fixable, but I have not bothered to do it because I only sync once a day.

You do need to obtain a key first though, which requires a login to the Xiaomi servers. I used a throwaway e-mail for the registration. Gadgetbridge has no access to the internet.

Only one I recall (smartwatch open source)

https://www.pine64.org/pinetime/

Does this fit the bill for you?

Garmin Fenix! The new ones are very expensive ($1000), but I picked up a used Fenix 5X a few years ago when it was the most recent model for $350 and I love it! Battery charge lasts about 3 weeks on mine and 6 weeks on the newest ones. It has sports tracking activities for just about anything you'd ever do, a great phone app interface, doesn't need to be charged for weeks at a time, and has GPS topo maps that you can use while backpacking, cycling , jogging, or even driving. I was able to track how far I paddled in my kayak thanks to the GPS. Anyways, it's a great watch if you're looking for a fitness tracker as well as a smart watch to give you phone notifications, music controls, and that sort of thing. The only drawback is that the screen resolution isn't great on the older ones since they use eInk screens instead of fancy screens. The new one uses OLED, so it's supposed to look better. Oh, and they're not touch screens. That was a little clunky for me when I first got it, but it doesn't bother me now.

Maybe a watch supported by asteroid os is something.

Some models have support for heart monitor. Don't know if there is a fitness app or something like that.

anything that's supported by Gadgetbridge https://gadgetbridge.org/

I like my Garmin gps watch, though they have gotten what i would consider too expensive...

I've been considering the Bangle.js 2, and while I don't think the heart rate monitor is really good yet, there is active development and discussion about how to make it better. If you're interested in helping out, this could be a fun project!

I'm pretty sure Garmin has a good privacy policy - mozilla seemed to like them - and I got a fenix6 sapphire on ebay used for about $250 and I love it. Way better than my apple watch, particularly because I care more about fitness tracking and hate having texts show up on my watch.