Why will Time Machine not restore Mail?
I have a new iMac running Catalina and I too found that I could not travel back in time when entering Time Machine from Mail (but it was OK when entering Time Machine from Finder).
The problem may be with backing up Mail messages.  During a Time Machine backup, the Console app issues unpromising messages including Couldn't create MailLibraryItem at path: /Volumes/com.apple.TimeMachine.localsnapshots/Backups.backupdb/(my mac)/2020-08-16-141340/Macintosh HD - Data/Users/(my user)/Library/Mail/V7
I have just spoken to Apple support, and their engineers are aware of the problem and are working on a fix, to be included in a future OS update, which is great news.
I appreciate that this reply doesn't help with the original problem, but the lady from Apple I spoke to did say that there may be other ways to restore lost email messages, so it might be worth your while calling Apple support.  Good luck!