I'm looking for advice on a privacy friendly fitness tracker. One that doesn't require storing my personal data on a third party site, where I can sync the data locally using an open source program. I do have a PineTime but it doesn't really track metrics and I question the accuracy of the heat rate monitor. FitBit is owned by google, and I don't want an Apple Watch. Any recommendations?
You're never going to get any sort of privacy with any device that runs WearOS because Google, and it can't be rooted.
Your best bet is an open-source smartwatch. I looked at true privacy-friendly, offline, open-source smartwatch options a few weeks ago, and my conclusion is that the only two viable alternatives are a PineTime or an older smartwatch running AsteroidOS, and none of the watches supported by the latter are sold anymore. So that leaves the PineTime.
Also, I wasn't looking for a fitness tracker myself, but the one thing that stands out with applications for non-wearOS smartwatches is that they're lackluster, to put it mildly. Fitness tracking with the PineTime is basically step counting and heartbeat monitoring. That might not be enough for you.