Issue is happening to me too and it appears to be totally random. I have confirmed my notification settings are correct.
I'll have received a text message but it won't wake the lock screen. iPhone 11 screen just stays dark. If I tap the screen to wake it I'll see the notification banner with the timestamp it was delivered at, but because it doesn't wake the screen or buzz, I won't know it's been sitting there.
You can imagine how big an inconvenience this is when you're expecting important messages.
And it's happened when receiving both SMS messages and iMessages. Some contacts will always show notifications, some won't. The ones that won't might work for a few days and then go dark again. As I said, appears to be a totally random bug.
The only fix I've found is to turn off Bluetooth (mind you I've tested it only once, with only one contact). Regardless, that is not a long-term solution.