My iphone doesnt play the text notification sound until I actually pick it up or screen lights up.
I’ll go to grab my phone or pick it up, and when I tap the screen there will be a new message in my Notification Center. The notification sound will come on at that moment but the message time shows it was from 3/4/5/6 minutes ago. There never was an alert sound when it actually came.
iPhone 11 Pro Max