After some further testing and observation I have some additional information that may give someone a clue as to what might be causing this. I will detail the issue again also just so this post is clear.
Before the Pie update, if I missed an alert, notification, text, email, phone call, etc. what would happen is this: After the initial alert or ring, I would start to get periodic audible alerts from my phone so that I would know that something was waiting to be read. A typical scenario would be... I am mowing the lawn and don't hear a call and an alert from our front porch camera. When I shut off the mower, at some soon point my phone would sound my repeating missed notification tone and I would know to take it out of my pocket and see what was there.
After Pie, the initial alerts/rings are happening in two ways. If it is a phone call the phone rings as normal, but if I miss the call, the repeating audible alerts do not happen every 60 seconds as they are set to and as they did before Pie. If the missed event is something like a notification from Kuna that someone set off the front porch camera, or an email or text then even the initial alert does not come through.
I have tested a few things and noticed that if I shut off the screen or wait until the screen goes to sleep and then immediately send an email, the phone alerts as normal. If the screen has been asleep for a longer length of time, then the alerts do not come through. It is as though there is an initial sleep mode after the screen turns off when alerts come through normally. Then after a period of time the phone goes into a deeper sleep mode where the alerts do not come through.
I have tested one aspect of this as follows. Sent an email from computer and wait a few minutes and see that no notification comes through. Wake up the screen and immediately the alert sounds. This was tested with Kuna also. Walked out the front door and set off the camera. No alert comes to the phone like it did before Pie. Wake up the screen and immediately the alert sounds.
Finally I have figured out today that if I do not unlock phone for a (unknown, but at least 15 or 20 minutes), long period of time, eventually an alert will come through. It is as if phone does know after a long time of sleep, to wake and check for notifications? Another thing I just thought of when typing this that may cause this last behaviour is my weather app. I have that set to refresh every 20 minutes I think. Maybe when that app checks and refreshes, that is enough to let the other notifications through.
It does seem like some sort of PIE battery saving mode is preventing the phone from checking for missed notifications and alerting once the screen goes to sleep. But in my settings I do have Battery Saver and Adaptive Battery OFF.