This actually does exist. While not a browser extension, if you use a Mac, just employ the Services menu. Highlight the text and then access Services and scroll down to where the Scrivener options are. Select Scrivener: Make New Clipping and it’s there. . It doesn’t do images, but there are other options for that (i.e. Add webpage to the Research folder or even Clippings.)
Scrivener has to be open to the project for this to work. That may be obvious but I mistakenly thought that Scrivener would open when this is attempted.
(Disclaimer: I didn’t find this on my own. I found it here: Have a look at Mac services. Scrivener offers a lot. (in “Scrivener as Web Clipper”.)