Very annoyingly, according to the official Microsoft docs the only way to convert an old .mdb file is to open it in Access 2003.
See section titled "
Convert an Access 97 database to the .accdb format".
Nice, but I don't have Access 2003. A crisp twenty to the first person who has a copy of Access 2003 handy and can convert the file! I think the file is Access 97, but could be 2000. Don't think that matters.