Sync Add On to sync 2 different Account (searched)

I am desperately looking for a Thunderbird Add-On in order to sync two independent IMAP accounts from within Thunderbird likewise syncing to folders with files (e.g. within Total Commander),

in order for example to backup “mail by mail” or just to check if a copying an account was succesfully done completely with each mail.

I know that there is software which copies complete accounts but this is not what I am looking for, I am explcitly looking for some way to compare two folders of two different accounts mail by mail.

E.g. You have one Gmail account and another account and you want to check if forwarding or copying is all done as ist should be.

Any help is apreciated. As I am new here in the forum I hope I didn’t oversea any discussion about this. Otherwise please let me know.