Should be possible using the Browser Toolbox to inspect the entire interface? I just checked and the HTML is definitely in the inspector at least, but I'm not sure what your requirements are.
The Browser Toolbox is the normal DOM inspector, just extended to the whole user interface. If you open the print preview, then open the Browser Toolbox, you can inspect the preview and edit styles just like any other document.
Also, @media print {} works fine, I just tested it. But I'm not sure how that relates to the original question.
https://imgur.com/a/S6XryYW screenshot of browser toolbox with the print preview DOM visible + site with @media print background color change. Note that you need to expand "More settings" in the print preview and enable "Print backgrounds" for that specific test to work.