You wrote:
“This would set the RCC apart from all other Christian Churches.”
The Catholic Church has always been apart from other Christian churches and sects.
Catholic Church was founded by Christ. Others? Founded by men.
Now, back to the point ~ the court didn't say the Catholic church is a state, just that the Vatican, which is a state, can be sued under a special law which can be used against other states.
I think there is currently an American Cardinal present at the Vatican (in a rather non-operative position) who is the real target of this lawsuit. He fled the US to the Vatican lest he end up sued down to his sandles.