Does CarPlay driving tasks entitlement support push notifications on CarPlay? If no, can Critical Alerts entitlement help in this case?

I am setting up push notifications in CarPlay and when the user taps on notification from infotainment screen, it should open the app and a CPAlertTemplate should be presented. How can I achieve this? since I'm unable to get a trigger on the didReceiveNotificationResponse so handle some custom actions in between.

I have set up an iOS application with CarPlay scene using carplay-driving-tasks entitlement. And as per latest policy changes I'm able to get push notifications in the CarPlay screen. But unlike from phone scene, when I tap on a notification from CarPlay I don't get a trigger on didReceive method to intercept the payload of the notification that user tapped on. Is there any other ways or configuration needed to get this working? I just need to get the payload and present an Alert template within the CarPlay when user taps on a CarPlay notification and the app opens.