Like you already assumed → the MENU-element has no → STYLE-attribute.
But what bamuu wanted to tell you is to add a STRIP behind your menu, or to describe it in another way → put your MENU onto the STRIP.
Now your MENU should be inside of the STRIP.
Change the DESIGN of your MENU to → TRANSPARENT (property-panel).
Now you can’t see the colors of your MENU, but you can see the backgroundcolor of the STRIP.
The STRIP-element has the → .style -attribute. Using this WORKAROUND, now you are able to control the backgroundcolor of the STRIP, simulating the colorization of your MENU.