I agree the Papal States is overpowered and needs a nerf.
50% extra tourism based on shared religion is too much, particularly since it can synergies so easily with Fealty. Pushing it back and weakening it makes sense.
I also think the disciples generating Great Works is not a good design.
So alternative pitch.
Apostolic See - Starts with a free shrine with new stages appearing automatically at religion milestones. Historic events generate faith. Birth of Great Prophets generates cultural GPP points.
The shrine stages, the UB which is granted for free.
(Settlement) Household shrine - 2 faith. Prevents construction of normal shrine.
(Pantheon) The Temple of Vesta - 2 Faith, 2 Art/Artifact slots, One filled with the Palladium. If slots filled, gain 3 faith and 3 Golden age points
(Founding) (Old) St. Peter's Basilica. 2 Faith. Spawns 2 free missionaries, and 25% extra strength. Two Great music slots, If slots filled, 3 Faith and 3 Culture. Gains (Old) title on Reformation.
(Enhancing) Lateran Palace. 2 Faith. Gain 1 Culture and 1 Gold for every city following. 2 Great Writing slots. If slots filled, gain 3 Faith and 3 Tourism
(Reformation). St. Peter's Basilica. 2 Faith. 1 Free Great Prophet. 1 Tourism for each Great Work. 25% extra tourism to shared religion.
This spreads out their UA and focused it more on being a tall civ. The papal state will get plenty of faith, though not as fast to a pantheon as India, and possibly Aztecs and Celts. But they ramp up over time as they work through Tradition. They get an immediate leap off on founding, with 2 free missionaries.
UU - Bishopric. Replaces Emissary, and never obsoletes. Has special action where it can establish a Bishopric on a city-state with a shared religion, increases pressure, making it harder to convert to other faith, and locked influence floor at Friend. Can also conduct normal diplomatic mission. Can be purchased with faith.
3rd and 4th UC
UU - Swiss Guard, fine as is.
UW - Vatican Museums. Seems fine as is.
Making it so that they can only settle puppets would be easy to add, and makes sense.