There is also the `undofile` option, which stores your undo-history permanently on disk. You can also go to an earlier version of the file from 4 hours ago with `:earlier 4h`.
Vim doesn't do it "well" with the settings above, just "good enough". The time stamp suffix is calculated just once when you start Vim, set in the global backupext option. If we :e edit files in an existing Vim session, they all get backups with that time stamp. It needs to be calculated as a buffer-specific value of that option, if there is such a thing, on every new edit.