Is it possible to delete the messages app from apple car play? (I have an iPhone SE, iOS16.1.1, and a 2021 Ford Ranger)

I believe the messages can only be deleted from your device and they still show on your car screen.

After deleting the messages from your iPhone, then disconnect it to the connection (USB or wireless) to Car Play.

Then connect it again.

Note:

If you want to hide your messages from prying eyes or don’t want show your messages in CarPlay, you can disable it from the notification.

You can't delete the following Apps from the iPhone

Photos, Camera, Clock, App Store, Health, Wallet, Safari, Phone, Message & Find My apps.

Regarding your Car, you may please see this link for help --> https://www.solveyourtech.com/how-to-remove-apps-from-carplay-on-an-iphone-13/