As stated before the backup dir is only used if the old state needs to be recovered. Feel free to delete after the update went successful and you notice no problems.
The .step file is usually removed during the occ upgrade or the web upgrader (the updater replaces code and the upgrader runs the actual migration steps of the new code).
So if you have problems with the updater just remove the whole updater-oc… directory and the updater doesn’t know anything anymore about any previous updater runs (which is fine if you don’t need the backed up code).