I know, that was actually my point, to know if anyone had tested this My concern is that maybe, within an extension (like Kantu), making network requests to something that does not belong to your domain (or the domain of the page) is not possible
The Javascript of storeEval runs in the context of the website. So it can do everything that the Javascript could do, if it were part of the website (that should include making network request).
As a test, you can check if it works in the Chrome browser console… if it does, then it should work with storeEval.