Thanks for that reply, @ddmiller. I think you’re on the right track in that the “above the line” notifications definitely tend to be the newer ones. But the details that you describe about lock/unlock don’t match what I’m observing.
But we may have some terminology to get straight first. Is what you’re calling “lock screen notification” the same thing iOS calls “notification previews” under Settings->Notifications->Show Previews?
In any case, there is no above the line / below the line situation when my phone is locked. The “Notification Center” banner with the (X), as shown in that screen shot, is not visible when my iPhone is locked (even though Settings->Face ID->Allow Access When Locked->Notification Center is checked; another mystery). I don’t have access to NC at all on my lock screen; just these “previews” of new notifications that have arrived since the last lock. So this issue doesn’t appear to have anything to do with the locking/unlocking.
Nonetheless, I did some testing.
With my iPhone locked, I had my daughter send me a text. I then unlocked my iPhone (but didn’t read the text). Then I locked it back up again. The text message is still visible on the lock screen. It didn’t go away because of the lock/unlock sequence, the way you appeared to suggest.
Repeating the above process with the phone Unlocked shows this new text above the Notification Center banner, and it stays “above the line” through a lock/unlock.
So, this remains a puzzle to me. And the two settings I mention here also leave me confused as to what they do.