Many things that we now consider staples of western magic are ideas that have been added to over generations by several layers of thinkers. Tarot Divination specifically is an excellent example of this!
In 1770, A french printmaker and occultist going by Etteilla published a book about how to do cartomancy with a 32-card Piquet deck. He writes down some simple but strict associations for the cards, and makes what is probably the first mention of reversals in carotmancy. He said that he learned the system "from an Italian." Now, its unclear how much of the system is his own invention, people have been doing cartomancy for as long as there's been cards, but the text presents a larval, bare-bones version of the cartomancy methods we know and love today.
Its 1780-ish. The Rosetta stone hasn't been discovered yet. Occult-inclined Europeans are obsessed with Egypt. That's where our boy Trismegistus is from! There's a concept in Egyptian mythology called The Book of Thoth, a mythical book of spells penned by the God of Knowledge himself. This was the Holy Grail for European Occult Egpytaboos.
In 1781, Antoine Court de Gébelin claimed that Tarot cards were the "original book of Thoth," Saying that Tarot cards had been used by ancient Egyptian priests for their own magical ceremonies, and that their designs contained ancient mystical secrets. This is 100% not true, but he writes a pretty fun pseudohistory for Tarot that involves Romani people bringing the decks to Europe through the Levant where they then taught its esoteric secrets to several Popes.
Then in 1783, Ettellia responded with another book. Manière de se récréer avec le jeu de cartes nommées tarots ("Way to recreate yourself with the deck of cards called tarots") Where Ettellia basically claims "uhm actually I knew about tarot divination way before Court de Gebelin published that big ass book. But anyway here's an interpretation of Tarot symbology that includes multiple references to Egyptian, Zoroastrian, and Greek mythology." But the smartest thing he did was include spread methods that involved Thoth and Numerology. Napoleonic Occultists fucking loved Thoth and numerology.
In 1788, he formed a little magical society for the express purpose of discussing and workshopping ideas for Tarot divination. In 1789, he made a TRULY smart decision, and published a Tarot deck that was Specifically For Magic, and that basically cemented Tarots place in magical history.
Occultists just kept iterating! Someone would speculate "maybe the suits correspond to the elements" and people went "yeah, they correspond to the elements! That makes this tool even more fun and interesting to use!" Then people go "What if the suits and the elements also correspond to parts of the Self?" and people went "Sure they do! That makes this tool even more interesting!"
But its also not just one thread. Eventually you get the Golden Dawn saying "The Major Arcana correspond to the nodes and paths on our version of the Quabbalistic Sefirot, you know, the hermetic version with a Q." and some occultists responded "Idk about that! Love what you've done with the color symbology though!"
The development of magical ideas is an iterative process. It is people whipping up a table of correspondences, but that table needs a mythology to keep it together. Originally, the mythology that gave tarot "power" was its Egyptian pseudohistory, but these days its the fact that occultists have been iterating on and fine-tuning this system for hundreds of years.
Humans don't think in tables of information, they think in stories. The cool thing about stories is that they're flexible. If magic is anything, its learning how to engineer stories to make the tables of information more effective.