Does the Back up drive partition need to be reformatted to accommodate these APFS snapshots?
I would assume so. I haven't tried using an external disk yet as I do my backups to a Synology NAS, but I've read that external drives are even faster. I do see a major improvement in performance with my NAS backups.
To give you a bit more background information: until Big Sur Time Machine utilised hard links. Essentially, each version of the file was only stored on the disk once, but this file was simultaneously present in multiple folders. So a backup would be a bunch of folders with a timestamp in the name, and contents of those folders would point to these files. This works, but requires that each backup is "assembled" manually, as links need to be set for each file separately.
In Big Sur, Apple is using native snapshotting functionality of their new file system, APFS. They don't need to build the link structure per hand anymore. They simply copy over a "frozen" snapshot of the filesystem metadata. This is obviously faster and much more robust. I would also imagine that new backups require less space, but this is something to be verified.
