The original Firefox sync worked like this (with a unique code and pairing instead of an explicit account) (this is so on the nose I suspect you may know this).
Didn't expect to click on that link and end up on a blog post I wrote 10 years ago! The old Firefox Sync / PAKE stuff was fantastic for getting sync going between devices... but people wanted backup, not sync. I wonder if we'd do anything differently confronted with the same challenge today.
This blog post goes over some of that history: https://blog.mozilla.org/services/2014/04/30/firefox-syncs-n...