"The Pope and the official Catholic Church" don't spend their days "identifying" Catholics. They have better things to do. Neither does the Church keep a list of who is and who is not a Catholic nor does it issue a membership card which identifies the carrier as officially Catholic with the Pope's signature and valid stamp.
There's a good reason for that.
It's because being Catholic entails interior assent to certain beliefs and the living out of those beliefs on a daily basis. Obviously, that's something that God can very well keep track of but it's a little difficult for mere mortals.
Individual parishes keep historical records of who was baptized, who was married, who died etc, but you'll appreciate that this is not quite the same thing and it's not a job for "the Pope and the official Catholic Church". The office workers take care of it and says nothing about adherence to those tenets of faith which the Church professes.
So the Vatican is not in any way a source for the number of Catholics?