I'm rather late to the party, but I've had this experience too. Make sure you unlock your phone when you plug it in. Even if you have "Allow CarPlay when locked", iOS's USB security has tightened up so you'll occasionally need to unlock your phone after plugging it in before it will let CarPlay run.
Most of the time, it's Get in -> Turn on Clarity -> Plug in iPhone -> CarPlay
Sometimes, it's Get in -> Turn on Clarity -> Plug in iPhone -> No CarPlay?? -> Unlock iPhone -> CarPlay
Let me know if that works for you.
There should also be a way to disable the USB security (though I recommend against it): Settings -> Face ID & Passcode (older iPhones is Touch ID & Passcode) -> Allow Access When Locked: USB Accessories -> Toggle to 'ON'
2018 Clarity PHEV Touring
Stock, save for tinted windows