You can't change background color in normal Rich Text Display fields, but a very-close alternative option would be to implement a "cards as tabs" setup which is also very common (and about the same level of difficulty as what you already have). Here's an example of a live robust implementation:

With this style of setup you'd have full control over the coloring and formatting of the tab (between "selected versus unselected" at least).
As an aside: the post title of just "user interface" is not very helpful or descriptive of your question (and has probably been used, verbatim, 50 times previously here in Community). I strongly urge everyone to create a unique (though still concise) post title that at least gives the flavor of the thing you're asking in your post, which would then contain additional details / screenshots / etc.