We're currently weighing up the pros and cons of switching over our iOS and Android apps to React Native, but would like to know whether we can integrate a React Native build with Apple's CarPlay and Android Auto?
Did you look at sharing extensions by any chance? I know it's not what you're asking, but I can assume the reasons why there's nothing for CarPlay/Android Auto are very similar.
Also, you may want to check this out, it could be a starting point to get your project working: https://github.com/alinz/react-native-share-extension