How do I recover old emails on Time Machine after Big Sur upgrade?

Hi judysings

Thank you for taking the time to issue support.

Because of my urgent need for the old email I called Apple support, and after a number of simple but failed steps I ended up with remote support logging on to my MacBook Pro and taking a look at my problem. They confirmed that entering time machine would only allow selection of dates from Big Sur backups, and that earlier dated backups performed by OS10.14 could not be read. The right hand list of dates and bars would go red for the accessible backups, but only go pink for the older backups. These backups were available but simply not readable by Big Sur. Support surmised that when Big Sur did its first backup on top of the already established back ups it was simply added; all previous backups were ignored and not updated to suit Big Sur.

Apple support showed me how I could open up these backups, "manually" pull out the emails then import them into Mail, which I did. Took some effort and time to import and sort out the email history but eventually I obtained my important missing email. All good!

This was my first use of Apple support after 25 years of Apple Mac ownership, and the support specialist told me that others had the same problem. I guess it is a software issue of some kind that either needs to be taken care of by Apple, or users will doubt the reliability of Time Machine. I have found other posts here and on other forums which have recorded this issue. I was impressed by Apple support.