How would these “rights” of a state be described, except as powers?
In post 101 you wrote: "States don’t have “rights.” They have powers."
If a right is described as a power it is still a right. If states have powers which are descriptions of rights, then states have rights.
If you're defining a State as a ruling regime (which I'm not sure I would), the ruling regime (State) has a right to rule (with the consent of those ruled) which right may be described as a power but even so defined is still a right, therefore states have rights.