Earlier quoted context omitted.
Obviously the browser has to provide this backend. Browsers already sync passwords, history, bookmarks, extension data, they should offer sync as a feature for the web app as well.
That's fine but then it's not really a feature of the web... it's a browser feature. You are totally locked into that browser. Compare to browser bookmarks. Not a "web feature".
These of course lock you into the browser (or the password manager) to the same extent. (Of course, just as a browser might support different password managers, so it might support different sync back ends.)