I called Customer Care. They checked a few things (apparently this can be an issue if you've ever changed the email address associated with your account) and then said a factory reset was necessary. A little annoying, but this did resolve the issue.... now we just have to set up all our settings again.
We also resolved my CarPlay issue, which... I'm not sure whose fault this problem is. When you pair bluetooth the car appears as "Lucid Gravity - 496", and while that shows up under "My Cars" it can't be used to connect CarPlay and blocks CarPlay entirely. If I delete that and don't allow Bluetooth to start, I see "Lucid Gravity - 2496" which then can pair correctly for Wireless CarPlay.

Why does one mode use 3 digits and one use 4? Surely someone's bug.