Backing up busy email server

I don’t have any experience with the challenges you write about but there are quite a few threads in this forum about backing up large datasets, like this one. Especially CERN are worth mentioning as they do huge backups using restic, are discussed in multiple threads and have quite a few CERN internal presentations about the issue available online.

From what I have read so far, most trouble with huge backups comes from having too little RAM available which, as you write, should not be a problem in your case.