Yeah, it make for a nice workflow, doesn't it. It doesn't give you the "fully automated" achievement, but it's not much of a chore. :)
Have you considered something like borgbackup? It does good deduplication, so you won't have umpteen copies of unchanged files.
I use it mostly for my daily driver laptop to backup to my NAS, and the Gitlab CE container running on the NAS acts as the equivalent for its local Git repos, which are then straightforward to copy elsewhere. Though haven't got it scripting anything like bouncing containers or DB dumps.