Apple is generally really good with privacy stuff. The health data stays on device unless you enable iCloud backup/sync. You can choose what app (if any) you’d like to share which part of your health data with (at which point you’re beholden by those app’s workflows and privacy policies). You can read directly from Apple here.

But the limiting factor is that you’d need to buy in to the rest of the ecosystem… or at least an iPhone. Not an issue for me, but YMMV depending on personal preferences.