Henry Cavendish reported in 1766 that dissolving metals in acid released a distinct gas, lighter than air, which burned to leave nothing behind but a dew. He called it inflammable air, and within the phlogiston chemistry of his day he took it to be phlogiston itself, or something close to it. He was working carefully and he was wrong, which is the ordinary condition of a good experiment inside a bad theory.
Antoine Lavoisier repeated the work, showed in 1783 that the dew was water and nothing else, and renamed the gas hydrogene, the water-former. That single result did more damage to the phlogiston doctrine than any argument, because water had been an element since Empedocles and was now demonstrably a compound. The four classical elements did not survive it.
It is worth being exact about what this means for correspondence. Hydrogen was not one of the seven metals. It was not one of the three principles. No alchemical symbol exists for it, because no alchemist ever isolated it or suspected it. Any chart assigning hydrogen a planet, a chakra or a sephira is doing so on modern authority, and the honest course is to say whose.
What can be said is that the substance alchemy called water, and treated as one of the four roots of everything, turns out to be two thirds hydrogen by count of atoms. That is not a vindication of the old scheme; the old scheme was wrong about water being simple. But it is a genuine point of contact between the two vocabularies, and it is more interesting than an invented correspondence would be.
Industrially, hydrogen now goes overwhelmingly into ammonia for fertiliser and into refining petroleum. Almost all of it is made from natural gas, a process that releases carbon dioxide, and the entire current argument about hydrogen as a clean fuel turns on that fact rather than on anything about the gas itself.