I've also been experiencing this on my 12 Pro Max running the official iOS 15.1. I haven't been able to figure out if there's a pattern (ie only when unlocked..), but most of the time I don't get a notification alert for my Messages. I'll just check my phone randomly and realize I have a bunch that came in... I verified that Notification sounds are on and Messages have instant alerts (with Repeat Alerts set to Twice even). Very frustrating!