ALL my 'custom' Mailboxes in Mail disappeared following upgrade to Big Sur

Until last week I have been running OS Mojave my 2019 21.5" iMac . I always use MacMail and have accumulated approx 18,000 emails which I have carefully filed in 30-40 'custom' mailboxes and sub-mailboxes within MacMail over a number of years.

This week I have changed my iMac to a 2020 27" iMac with a 512GB internal SSD AND also, at the same time, I upgraded the OS to the latest Big Sur 11.4.

Unfortunately, once the new OS was installed I found to my horror that all 30-40 mailboxes had 'disappeared' even though the emails themselves appear to remain - but they are now dumped into one single huge mailbox (called "Important") and all my careful custom-filing 'organisation' is totally lost!

I have tried to use the Mac 'Time Machine' to recover the mailbox structure but it will not open at all, because, I think, as it is now sitting in a 'new' environment in the new SSD and not the old external HDD, it does not recognise the new installation.

I see that many others have suffered very similar issues and I'm horrified that Apple has not jumped onto such a fundamental problem that is very important to the vast majority of users.

I also run CarbonCopyCloner and I am hoping that the back-ups there might just contain the file structure that I have lost.