Everything twenty-two does in the Western esoteric tradition comes from one fact: the Hebrew alphabet has twenty-two letters. The Sefer Yetzirah divides them into three mothers, seven doubles and twelve simples, and treats them not as notation but as the instruments with which the world was made, carved and hewn and weighed and exchanged. Josephus, writing for a Greek-reading audience, counted the books of the Hebrew scriptures as twenty-two as well, matching the canon to the alphabet.
Later kabbalistic diagrams give the Tree of Life twenty-two paths joining its ten sefirot, one for each letter, so that the number of connections in the diagram is fixed by the alphabet rather than by the geometry.
The tarot arrives at twenty-two by a completely separate route. The Italian card game that produced the pack has twenty-one trumps plus the fool, a structure with an obvious reason inside the game and no reason outside it. That the two counts match is a coincidence, and the identification of the trumps with the Hebrew letters is a nineteenth-century French proposal, taken up and systematised by the Golden Dawn, which then rearranged the correspondences more than once. Dummett's history of the pack shows the game and its trumps to be a fifteenth-century Italian invention with no esoteric content and no Hebrew connection whatever.
The pairing is now so embedded that it is usually presented as ancient. It is a claim with a date, and the date is recent.