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.