"In cases affecting Ambassadors," one idea separated from another idea by a comma then "other public Ministers and Consuls", yet another idea separated by a comma, then "and those in which a State shall be a Party", yet another separate idea with a comma separating it from the previous ideas.
If the Founders meant what you say why didn't they simply write "If a case has Ambassadors, public Ministers and Consuls and a State the Supreme Court has jurisdiction"?
No, those are all separate ideas and only a Lawyer could read it otherwise.