I have made a not so elegant way to do this but any one who can improve upon this or give an better solution should do so.
I'm using gist by Github for broadcasting my battery percentage first to a private file, tried using ix.io which is what I usually use but pkg install ix didn't work on Android terminal the config.guess threw and error saying unable to ...
Some OEM ROMs offer such a functionality, most do not. You can check your device's settings, if there is such an entry. If there is none, then it is not possible. So, the answer to this question will be a yes and no together. It will depend on which smartphone you have.
You can certainly not achieve this with 3rd party apps.
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
Bluetooth event → Device connected → your car device
Priority mode/Do not disturb → select one of the options - Allow priority notifications or Block all
Name and save the macro