Every 6 months or so I go looking for a solution to this problem and still haven’t found one.
When my phone (Pixel 7) is connected to my car by bluetooth, the phone itself will not make any notification sounds. It is attempting to send all notification sounds to the car. The problem is, if I am currently not listening to any media and the head unit is off, I will not hear anything at all. The only possible way to hear it, is to have the head unit on and set to bluetooth input whether or not I’m listening to anything. This was not always the case. I think it changed after Android 13 was released but I’m not 100% sure.
A head unit is the actual radio hardware in a car. Some of them can be replaced with after market hardware. Yes, when my phone is connected to the radio by Bluetooth, I have to keep the unit on and set to the Bluetooth input in order to hear notification sounds. If I have it off, or set to another input I won’t hear any notifications that come in.