Edit → Find & Replace allows to search for paragraph styles, which is handy to spot erroneous use of paragraph style (according to local conventions). But the same cannot apparently be done for character style.
Is this a design decision? Or is the feature hidden somewhere else?
The same question could be asked for frame styles.
The case of page and list styles is less critical since they are applied relatively less often. A page is easy to spot and list styles are in principle associated with a paragraph style and this can be checked through the style navigator.