Why doesn't it work for graphic styles?
Dragging objects with colors and styles assigned from tab to tab may be the most expedient way.
You can save Graphic Styles and open them in a new panel and make the panel Persistent. This keeps them available for all documents you open and work on.
Set up all the graphic styles you need to use through out the documents or project. In the Graphic Styles Panel use the menu in the upper right and go Save Graphic Styles Libaray…, then in this same menu go Open Graphic Styles Libaray>Other Libaray, and navigate to where you saved the Graphic Styles. Once open in a new panel use the menu on this panel and select Persistent.
You can open the Libraries of any file by using the Window>Libraries(Graphic Styles, Swatch, Symbol, Brush)>Other and navigate to the file in question. In the old days you could keep one file of patterns and colors open in the background and they would be avialable to all new files.
Sorry, my bad - it works with styles when one copies/drags objects between tabs...
Having a persistant style library saved works, but only partly - if I want to modify/add styles as I go along, one has to add it to the main Graphic styles panel, and then save it as a library again, then close the library panel, and re-open it...
I guess another way to work with this would have been to have all four illustrations that I need to do in one document, but with multiple artboards, then I would have all styles and swatches in one place.