I'm guessing today is the most common birthday for popes. 
We'll let Tony research it.
ChatGPT is being a pain in the ass with, "due to incomplete historical records, especially for early Popes, determining the most common birthdate among all 266 is not possible." Yet, it also tells us that no date exists where a birthdate is shared by four or more Popes. So CigarBanter is going with today.