the files are within the (Internal Storage) space, under path: MIUI/backup/AllBackup/YYYYMMDD_HHmmNN, where Y is year, M is month, D is day of month, H is hour (24H), m is minutes, and I don't know what N is. Perhaps seconds.
You can easily copy the file, but I've not verified you can them simply copy them to another phone (or to your phone after a ...
You already answered your question yourself. Last backup has been overwritten by new backup. There is no way to get last backup without having old phone.
Local WhatsApp backup is located Internal Storage
transfer whole directory to new phone
install WhatsApp (or clear app data)
restore local backup on initial setup