I add styles support for text context menu. You can add defined styles for text and can add also additional styles via configuration menu. Have this functionality for shapes would be awesome, but there I would prefer to have all used document shape styles so that you can use always the same styles. draw a shape -> right click -> style -> recent document style list
Are you aware that shapes in Writer and Calc currently have no style but only direct formatting?
Created attachment 146240 [details] right click on shape right click on a shape you can have an section for the shape styles (or shape direct formating) which are used in the document.
So you do not want an access to styles but to the area filling. I think, that such a row of "fillings used in document" would be better placed in the area section of the properties pane in the sidebar. It would have a benefit about the area dialog, if it lists all kind (color, gradient, hatch, bitmap) of fillings in one row. I personally do not like sub-menus in the context menu.
As Regina said, context menu sub-meta items should be avoided as they lengthen the mouse action so that the user also can use a toolbar or sidebar instead. But I think of a kind toolbar like in bug 119707 (Introduce "mini toolbars" attached to context menus) where such colors can be shown.
I think we can close this one as - we haven't color support in any context menu yet (why then here?), - such concept needs a completely new implementation, which can better achieved by bug 119707, - Style is not the right name for this, - more properties than in the context menu are shown in the sidebar.