The restricted mode of Car-Play creates issues of detection. You can reset these settings by going to the settings mode. Select the screen time with privacy restrictions and tap on the allowed apps. Make sure that the Car-Play is enabled now. You can then again go to the settings and, from there, select the general and car-play modes. Tap on the car and press the button to forget this car. In this way, you can set up the Car-play again.