I already use Firefox for browsing normally, but I have to test on a Chromium based browser too. One soft requirement is that it should be installable with Flatpak on Linux.
Yes. https://www.chromium.org/Home/chromium-privacy/
But not nearly as many tracking mechanisms as Chrome, because it lacks API keys for some services. By default, it will still send the URL of every page you visit to Google, though. At least that’s my understanding, reading their privacy policy.
But it also doesn’t update itself, doesn’t seem to have a working Mac build (the one on their website doesn’t launch), and doesn’t sync (which I can live without, but end-to-end encrypted sync is nice).