I have my pixel 4a connected to the car via Bluetooth and all permissions granted. In the car settings for SMS I have the "show message alert" option checked (or whatever it's called) yet when I receive an SMS I get no alert in the car. Nothing audible and no on screen message etc. Only way I knew I had an SMS today was my phone vibrated in my pocket. So I went into the SMS section of the phone app on the car and sure enough, the SMS was showing in there. So the car can obviously see the messages, it just doesn't alert for new messages. It was a "true" SMS as well, not an iMessage to Android, nor a Google message to SMS etc.
