Our web edition and mvc edition should support the feature you mentioned like when hovering a shape, highlight it.
But the feature is supported by client side library.
So if you are using WebAPI Edition, you should want to implement that by your custom code, our server side only return the shapes you need, but for the special feature, you should research the client side library for support.
Our WebAPI mainly provide GIS features, it have more agile, and need more custom code at the same time.
For example you can return tile images from server side, or you can get the features included by target extent and return them and styling them by your styles.