Judah Benjamin diagrees with your charaterization of "formal" relations:
Excerpt from a letter from CSA Secretary of State Judah Benjamin to Dudley Mann, CSA envoy to the Vatican, Richmond, February 1, 1864:
"The President [Jefferson Davis] has been much gratified at learning the cordial reception which you received from the Pope, and the publication of the correspondence here (of which I send you a newspaper slip) has had a good effect. Its best influences, as we hope, will be felt elsewhere in producing a check on the foreign enlistments made by the United States. As a recognition of the Confederate States we can not attach to it the same value that you do, a mere inferential recognition, unconnected with political action or the regular establishment of diplomatic relations, possessing none of the moral weight required for awakening the people of the United States from their delusion that these States still remain members of the old Union. Nothing will end this war but the utter exhaustion of the belligerents, unless, by the action of some of the leading powers of Europe in entering into formal relations with us, the United States are made to perceive that we are in the eyes of the world a separate nation and that the war now waged by them is a foreign, not an intestine or civil war, as it is termed by the Pope. This phrase of his letter shows that his address to the President as "President of the Confederate States" is a formula of politeness to his correspondent, not a political recognition of a fact. None of our public journals treat the letter as a recognition in the sense you attach to it, and Mr. Slidell writes that the Nuncio at Paris on whom he called had received no instructions to put his official visa on our passports, as he had been led to hope from his correspondence with you.
"disagrees with your characterization ..."
Good night.
The message you quote from Benjamin came before any significant diplomatic events other than the first visit of A. Dudley Mann a month earlier. Mann had sent Benjamin a copy of the pope's proclamation, arguing that it was indicative of diplomatic recognition to which Benjamin expressed his disagreement. Despite this, both after Mann's first letter and over the next several months, Cardinal Antonelli became openly receptive to CSA diplomacy, indicating that the recognition was of the nature Mann described. He granted diplomatic protection to Mann and other confederate envoys. After Benjamin's letter, Bishop P.N. Lynch of Charleston even served as a formal diplomatic intermediary between the two and the CSA granted him full recognition as their envoy. Antonelli continued to recieve CSA diplomats throughout the year and, in a following letter from November 1864, spoke of the confederate "government," "president," and the war that was waging between the "two countries." Such is indicative of clear diplomatic distinguishment. Thus, it appears that Benjamin drew an erronious conclusion at an early point in diplomacy before it had the opportunity to develop.