As said previously, Borg is a full dedplicating incremental archiver complete with compression. You can use relative paths temporarily to build up your backups and a full backup history, then use something like pika to browse the archives to ensure a complete history.
Tbf you did start your post with
So you’re going to end up with at least a few people talking about how to onboard your existing backups into a proper backup solution (like borg). Your bullet points can certainly probably be organized into a shell script with sync, but why? A proper backup solution with a full backup history is going to be way more useful than dumping all your files into a directory and renaming in case something clobbers. I don’t see the point in doing anything other than tarring your old backups and using
borg import-tar
(docs). It feels like you’re trying to go from one half-baked, odd backup solution to another, instead of just going with a full, complete solution.