Article III, section 2, clause 2 of the Constitution says
In all Cases...in which a State shall be Party, the supreme Court shall have original Jurisdiction.
I would interpret this as meaning that when a state is the plaintiff, the Supreme Court should have original jurisdiction regardless of who the defendant is. But this is not the case — to give a recent example, in Trump v. Hawaii, Hawaii filed suit in a district court. Why do lawsuits by states not invoke original jurisdiction of the Supreme Court?
This is not a duplicate of this question, which concerns lawsuits between parties that are explicitly stated as not having original jurisdiction. It does not address the question of a state as a plaintiff.