Icon color from device class does not apply to badges?

If I have sorted out all the changing advice on setting icon color up to the most recent updates, apparently it still can’t be done without installing Custom UI, correct?

If I select device class “safety” for my binary sensor in order to use the built-in icon colors, the icon is supposed to change between black and yellow (although red would probably have been a better choice given the number of icons that are routinely yellow in the UI). And it does change color, if included in a Lovelace card. But it doesn’t change color when it’s a badge. Is that correct, or have I missed something?