Those are not Commonwealth coins. They call ruler Frederick August (D G FRID AUG REX POL DUX SAX ARCHIMARESCHALL & ELECT) in obverse, refer to Saxony (IN PROVINCIIS IUR SAXON PROVISOR ET VICARIUS) in reverse and they are minted in main Saxony mint. Just cause countries share ruler or king title is higher than duke does not make Commonwealth entitled to claim ownership of these coins. Only in some cases Commonwealth pages provide details like diameter or weight that are not available in Saxony directory. They also confuse HRE with Germany. Austrians, Hungarians, Czechs and Croats might have some words about how German they are.
https://en.numista.com/catalogue/pieces258659.html
https://en.numista.com/catalogue/pieces258669.html
https://en.numista.com/catalogue/pieces258672.html
https://en.numista.com/catalogue/pieces125791.html
https://en.numista.com/catalogue/pieces122901.html
https://en.numista.com/catalogue/pieces125757.html