Aah, so others are having issues too with their 11 Pros and CarPlay. I also have a weird thing with my BMW's wireless CarPlay. With my iPhone X CarPlay would always automatically connect and start when I would unlock my car. However with the 11 Pro CarPlay doesn't start. I see that it's connected to the CarPlay's Wi-Fi and Bluetooth, but it won't start. When I disconnect Bluetooth on my 11 Pro and then reconnect again, CarPlay almost immediately starts and all is fine. So I'm not having sound issues, just connection issues.
With my old X and my wife's 7 Plus it works flawlessly, but with my 11 Pro it doesn't. All devices are on iOS 13.1, so it seems specific to the 11 Pro for me.