Is there a setting on the new do not disturb feature that allows for notifications only to be silenced when the screen is locked? I can’t figure out how to get notifications while i’m on my phone

I’m trying to figure out how to have do not disturb so that my phone doesn’t light up with notifications but if i look at it it tells me what notifications I’ve received, and so that once my phone is open I get notified as normal. Does the new ios/focus mode just not allow it? Right now I can only see my notifications if i swipe up on the notification center or check for the red dots. thanks!