App Notifications Not Working after iPhone Upgrade

I upgraded my iPhone 12 to an iPhone 14 using the direct device-to-device transfer. Both phones were running iOS 16.1 at the time. Everything appeared to transfer from the old device to the new device correctly. I did not erase my old device right away; I turned it off. I spent a day with my new device, checking for photos, calendar information, and data related to apps -- all good! I got some Apple News notifications on the new phone, however, I did not realize that I was not getting all my expected notifications from a variety of other apps.

Obviously, the old phone had a SIM and the new phone has an eSIM. Calls work fine.

[As an aside, during the data transfer, I left the room wearing my Apple Watch. This result was, apparently, that my Apple Watch remained "paired" to my old phone. I discovered this later in the day, because I happened to try doing an Apple Watch screen shot. I had to turn on my old phone; unpair my Apple Watch; turn that phone off; and pair my Apple Watch with my new phone. That resolved it, but 5 hours of activity data was lost, going to my old phone.]

When I turned my old phone on the next day to erase it, I received dozens of notifications from various apps, which was disconcerting, given that the old device was no longer connected to my phone number. I erased the old phone, which, as expected, removed the old device from Find My and iCloud. The old device is no longer connected to me in any way. In fact, it's been traded in to Apple, and one of you might end up owning it in the future.

I changed the name of my new device from "My iPhone 12" to "My iPhone 14". This change percolated to iCloud and my other devices within an hour or so.

I continue to get notifications on my new phone from Apple News. Also, Sun Times and NFL notifications came back after a few days. But, I am still not getting notifications from about a dozen other apps -- other local media apps, sports teams, and notably, SmartNews.

I have tried the following, with SmartNews: Turned off notifications; deleted the app; re-started the iPhone; re-installed the app; and turned on notifications. No luck.

I am reluctant to sign out of iCloud and sign back in again because it creates the hassle of having to re-authorize all the cards in my wallet. I may do it as a last resort.

Has anyone else had this same problem, and resolved it? Will it resolve over time? By the way, are notifications tied to the phone number, device name, serial number, or EID?