It's a clever idea and it's super simple

Add an event listener on the entire document.body

Get the event.target and the style and then descend to the children. Put it formatted in the clipboard.

Then do it as a bookmarklet and deregister the click handler when you're done so you can continue interacting with the site

It's probably around 12 lines of modern js.

You can add a fancy graphical outline to know what you're selecting with a few more lines. Just make sure you draw it on top and don't modify the elements. Use a css filter to make it work on all elements.

Modern tooling is pretty great.