https://zenit.org/2024/08/29/vatican-citys-immigration-law-one-of-the-strictest-in-europe/

Vatican City’s immigration law, one of the strictest in Europe

In May 2023, Pope Francis approved a new Fundamental Law for the Vatican City State, reinforcing strict criteria for citizenship and residency. This law stipulates that Vatican citizens include the Pope, cardinals residing in the state, and individuals whose roles are essential to the Vatican’s functions. Residency, similarly, is granted under tight conditions and can be revoked at any time, underscoring the transient nature of living within the Vatican. Marriage and family ties offer no guarantees for continued residency, with the law stating that permissions for spouses and children cease under specific circumstances, such as annulment or separation. Furthermore, children of Vatican citizens lose their citizenship upon reaching adulthood, unless specific conditions are met.

So now we have Trump aiming to score political points by trying to project an image of restrictive immigration policy while continuing to run permissive policy and the Pope aiming to score political points by trying to project an image of supporting permissive immigration policy while running restrictive immigration policy.

EDIT: I see that someone else pointed out the same thing.