The page's scripts can indeed see and alter the changes you make to the DOM, but cannot access the extension's script or data, so there isn't much risk actually.
Extensions are protected by a mechanism called Xray vision, not the shadow dom.
https://developer.mozilla.org/en-US/docs/Mozilla/Tech/Xray_v...
Why does that matter if the content script doesn’t have privileged access to anything itself?
Because one can monkey-patch any JS function used by the injected script, as the OP showed, to make the injected script do whatever it wants it to.
By one, you mean the website that the script is running on right? What's a possible attack vector there? I didn't understand how an attack might work from the example in the article.
If the domain of the site is checked by the browser extension outside the content process, injection of the password is initiated by the extension button not a button on the page itself so there is no API the content process has access to, and only the correct password for that domain is provided to the content script, what could the page do exactly that would be a security issue? The content process would just be responsible for receiving any password injected into the page and putting it in the righ place.
Any PM that injects a script into the DOM is vulnerable, as the article explains, because the script runs with the exact same privilleges as everything else in the DOM (so the existing DOM can mess with your script or with the changes your script tries to make).
Also, the shadow DOM has nothing to do with security in any way. It's trivial to work around it whether it's closed or not. See https://blog.revillweb.com/open-vs-closed-shadow-dom-9f3d742... for example on how to do that.