Dropdowns are useful, but they would be even more useful if the dropdown options could be formatted. For example, using bold or italic text for various selections, or changing the background color of other options on the dropdown display.
It's easy to have a cell formatting change according to the dropdown selected, but that's not what I'm trying to do. I want the formatting of the the dropdown items to be different than simple plain text.
It sounds like you are asking for a way to change the appearance of the control that appears when you click the dart in a drop-down cell. The built-in controls in Google Sheets cannot be customized that way.
To implement your own custom controls, use Apps Script to implement a custom dialog box or a sidebar.