Will he be taxed on his foreign Papal salary? Or will he forego the salary , like Francis did?
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There's also the interesting question of whether he will remain a US citizen after all, or whether taking the office of pope will count as him relinquishing US citizenship under INA §349(a)(4): https://travel.state.gov/content/travel/en/legal/visa-law0/L... In the latter case, the tax question would not arise.
Existing US Department of State policy applies an administrative presumption to most cases of accepting foreign government employment that the person does not intend to relinquish US citizenship unless they affirmatively state otherwise, but they don't apply any such presumption to becoming a foreign head of state or a foreign head of government. They actively analyze such cases individually with no default presumption.
Pope Leo XIV will lose his US citizenship due to his acceptance of the papacy if and only if he intended to relinquish US citizenship by that act, based on the standard of proof of the preponderance of the evidence (the same as in civil lawsuits). He has the right to dispute the question in court if he and the US Department of State disagree on the answer, but I imagine this would in practice be handled more quietly for such a high-profile case.
Two examples from Canada: former Governor General Michaëlle Jean, who represented the Canadian monarch in Canada for day-to-day head of state duties, renounced her French citizenship when before becoming Governor General; and current Canadian Prime Minister Mark Carney renounced his British and Irish citizenships before becoming Prime Minister. Neither renunciation was required according to law or constitutional convention, but they both wanted to remove any question as to their allegiance.