This only works if the web page knows the random per-install id associated with an extension.

That can only happen if the extension itself leaks it to the web page and if that happens, scanning isn't necessary since it already leaked what it is to the webpage. It also doesn't tell you what extension it is, unless again, the extension leaks it to the webpage.

The attack on Chrome is far more useful for attackers as web pages can scan using the chrome store's extension ID instead.

And this bug was reported eight years ago, with no serious attempt to fix it since.