My point is that it doesn't need to sync. Ignore syncing. I'd even prefer to download and upload the backups by hand, rather than put it all in someone else's control in a browser environment.

Cloud password systems are like running all your security-sensitive code in an Electron app - an impossibly large attack surface with many significant flaws in some of your most-sensitive use. It doesn't make sense if you care about security at all. At least extensions are moderately well sandboxed compared to websites (since it'd be trivial to ship new javascript from their site).