I’d be happy either way. If the next backup job just continues where the aborted job left off, that sounds ok because it should only be broken for a day or so until the next backup job completes.
But, it seems slightly safer to allow us to restore anything that has been backed up. What if we need to restore one of those files, which is technically backed up and sitting on our backup server, but just wasn’t part of a “complete server backup”? It would be sad if the backup software told us “you’re not allowed to restore that perfectly available data because I said so”. It should probably allow the restore but just warn us that we are restoring from an incomplete backup.