Well… I don’t know whether to laugh or cry. Or both. I tried deleting one of my email accounts and re-creating it - no change. Then as per Bear7962’s suggestion I deleted the Mail app, rebooted, and reinstalled it. The first pleasant surprise was that I didn’t need to recreate all my email accounts. The second was that I do now get sounds when a new email comes in - whoopeee!!! But after 2 days of joy, despair… I now don’t get any notifications on the Lock Screen when a new email comes in, so I have to unlock the phone and go into the mail app to see which account the email is in and who it’s from to decide whether I need to read it pronto. Notification settings are all correct, and it all worked correctly for 2 days after reinstalling the app…
Is it really so hard for Apple to produce an email app which works reliably? It did for years, but now it’s just buggy.