Many people such like me are having problems by theming the carplay exclusive icons. I tried many things and wasted so much time by searching an working solution. First of all: The carplay icons are stored inside an Assets.car - On iOS 10-12 its stored in SpringBoard.app (/System/Library/CoreServices/SpringBoard.app). On iOS 13 its stored in CarPlay.app (/System/Library/CoreServices/CarPlay.app). So the normal way would be to edit the Assets.car file, but this can be a big problem if you are an windows user and don´t have any chance to using an mac for this. So because of this you will need an tweak that is able to theme files inside an Assets.car, this feature was available in previous versions of Anemone until CoolStar removed it. Also snowboard with it´s extensions is unable to do this. The theming engine you will need is iThemer.
You have to store your themed icons inside the SpringBoard bundle (iOS 12) or CarPlay bundle (iOS 13). Note: the home icon doesn´t need anything in it because your car will add the inlay automatically. The home icon is called "CarDisplayCanvasIcon-com.apple.cardisplay.OEM.png" and the Now Playing icon is called "CarDisplayCanvasIcon-com.apple.cardisplay.nowplaying.png". Both icons are having a resolution of 180x180px, i haven´t tried any other resulutions but i think you are able to use bigger files for an better quality.
CarDisplayCanvasIcon-com.apple.cardisplay.OEM.png & CarDisplayCanvasIcon-com.apple.cardisplay.nowplaying.pngTheming path:
(iOS 12) /Library/Themes/yourtheme.theme/Bundles/com.apple.springboard & (iOS 13) /Library/Themes/yourtheme.theme/Bundles/com.apple.CarPlayAppResolution: