Vatican did not declare a "Just War"...as I said, the Catholic Church pushes for Peace...Always...but provides a checklist for nations to consider...and Act in Accordance with, should the circumstances become overwhelming for them. If you weren't so literal...i.e. Black and White...you might have figured this out for yourself. If the RCC picks a side, it's lost its objectivity...and standing as a Peace Seeking Entity.

Good Heavens, you can be incredibly dense...and devoid of any ability to comprehend nuance....here's an overview of how the RCC dealt with this issue during WWII...
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AI Overview
The Vatican did not formally declare Allied military actions to be a "Just War" during World War II. While the Holy See maintained a policy of official neutrality throughout the conflict, Pope Pius XII and Vatican diplomats engaged in complex, behind-the-scenes actions that included sharing intelligence with the Allies, while avoiding public condemnations of the Axis powers that might worsen the plight of Catholics in occupied territories
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Key points regarding the Vatican's stance:
Official Neutrality: The Vatican sought to maintain neutrality to protect its status as an independent entity and to act as a potential mediator, which precluded labeling either side's military actions as entirely "just"

Proportionate Defense Concern: The Catholic Just War Theory requires that war be a last resort and that force be proportional. The Vatican grew increasingly concerned with Allied tactics, specifically the "obliteration bombing" of cities, which Catholic theologians later condemned because they believed the evil means did not justify the end, even in a defensive war
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Moral Concerns vs. Propaganda: While Allied powers sought a public condemnation of Nazi atrocities from the Pope, Pius XII believed that explicitly naming one side would cause further atrocities against Catholics and Jews by the Nazis, especially as he felt he would also have to condemn Soviet actions .

Post-War Recognition: In 1944, after the liberation of Rome, Pope Pius XII did meet with and bless Allied soldiers, acknowledging them as liberators of Rome
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Note: In 2022, Pope Francis stated that the concept of "just war" should be rethought, noting that "wars are always unjust" and suggesting that in the modern era, traditional just war framework does not apply
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