How to activate 'Do not disturb' when connected to a specific Bluetooth device
As you guessed, you need an extra app and in this case automation app. 

MacroDroid is easy to learn and free up to 5 macros. You need one macro

Trigger

Bluetooth event &rarr; Device connected &rarr; your car device

Action

Priority mode/Do not disturb &rarr; select one of the options -  Allow priority notifications or Block all 

Name and save the macro



You would need to manually disable DND mode once you are out of your car BT range or create another macro where the trigger would be BT event &rarr; Device disconnected and in the action whatever you wish, likely allow all