Clearly Apple, Harman, and Mini don't care. It's an issue for such a small subset of people that they just aren't worried about it, if they're even aware of it.
I know it has something to do with the WiFi chip (or the coding specifically for the new chip), because the issue wasn't happening on my XS on iOS 13, but it's been happening through all of the rapid updates on my 11 Pro since day one. Had the phone for 2 months and I can't use wireless CarPlay in my Mini, which is one of the huge reasons I went with that brand over my usual Hondas (that and a manual transmission available with other bells and whistles, which I couldn't get elsewhere).
I've switched to just using Bluetooth for audio, since there's no skipping. I'm guessing it's some odd bandwidth issue with WiFi direct connections. It's really a shame, because I love CarPlay and I love not having to take my phone out of my pocket to use it. It's a big enough shame that BMW/Mini won't allow us to turn off their split screen feature (that I don't care for at all) and use widescreen CarPlay, but now it just isn't worth using at all.