No email alerts on iPhone 16 Plus until Mail app is opened

My wife's new iPhone 16 Plus receives reports of text/SMS/iMessage receipt (sounds and banners) but NOT emails. The emails are arriving OK, but no notification - banner or sound - until email app is opened. The 16 Plus is an upgrade from her previous 14 Plus, which developed the same problem shortly after purchase. Having transferred data to the 16, I can only imagine this is a software problem, but I cannot track it down. I took it to an iStore locally and the staff member said "Mine is the same, it drives me mad." Wow, what service!

The sounds selected are standard sounds, nothing out-of-the-ordinary. I have previously visited an Apple Store, who had the 14 Plus for an hour and lost all my photos without fixing the problem. Phone network settings reset, all the usual trouble-shooting steps I'm aware of, but no success. Love the phone, hate the malfunction. Can ANYONE assist?

[Re-Titled by Moderator]

Original Title: iPhone 16 Plus not notifying receipt of emails