Alas, no. nix-on-droid runs in a proot, not as actual root. I've been meaning to put together something with actual root which reaches into nix-on-droid and does some kind of sync, but I'm not quite there yet.

My point is that synchronizing state between applications is not a problem that's unique to browser, and I'd rather use a generic tool for it.

If each application implements it's own sync mechanism that's just a lot more work overall.