The "cases and controversies" language of the 1st paragraph prohibits federal courts from rendering decisions where the parties don't have a dog in the hunt, while the 2nd paragraph limits the original jurisdiction of the Supreme Court to the types of cases enumerated.
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction.And the ACA is binding upon the states, therefore the States must be a party. (And in this case, so are the federal government, and the peoples of the states as well.)