Having this very same issue.
Followed your steps; removed and re-added devices in bluetooth and carplay, I have received the update but still having the same issue. Every time I connect there is no issue with charging 100% of the time.
My previous phone iPhoneX (pre ios13) worked perfect without issues, new iPhone 11 pro (ios13+) cannot get it to connect consistently. So frustrating, I do believe this is an iOS problem though.