When new email message received Mail used to, 'Ping', the right/top of screen showed incoming message header and Mail Icon should number of messages received.
This has not being occurring, although occasionally one or two parts do!
Important email message, which was replied to, was found in 'Inbox' & 'Sent' message folders without any of the above occurring, so did not know it had been received.
A small blue number appears under the message date, showed a reply had been received.
Apple contacted and after a couple of 'Chats' and 'conversations' they looked at Talktalk issues and advised a number are being shown, so maybe down to them. Asked to keep an eye on situation.
Anyone, especially Mac users after upgrade, having any similar issues or possible ideas as to what is occurring?
I think you've done the troubleshooting and found that the issue is with Apple Mail / Mac Mail Notifications.
You've found a message in the Inbox so clearly the Mac Mail client is working with TalkTalk Mail ok and retrieving mail messages from the online TalkTalk Mail Inbox and delivering them to the Mac Mail Inbox.
Have a look at the Mac’s Notification Center preferences by opening System Preferences, clicking Notifications and selecting the Mail client. Maybe those have changed with the recent update.
Nothing untoward noted here, although upgrading to macOS Catalina has in other respects been a bit of a learning curve!
As @Gondola suggested check your notification preferences and also check the General preferences within the Mail application itself.
Ah well I think the reason has been found!
After some impressive assistance from Apple, still being looked into further....
Where 'Rules' have been applied so emails arrive into 'On My Mac' as apposed to 'Mailboxes Inbox' they don't activate any notifications, i.e. sound, display number on Mail Icon or pop up on screen.
They are now being highlighted in 'On My Mac', so at least I know there are new messages.