Physical alchemy, or exoteric alchemy, as the precursor of modern chemistry grew out of crafts such as metallurgy and fabric-dyeing in China, India, and Egypt. However, the association of planets with metals can be traced back to Babylon, and the intermingling of astrology with a scientific understanding of plants and their uses has been called “magic” at least as far back as the early Roman Empire. Both physical/exoteric alchemy and spiritual/esoteric alchemy were, for a time, one and the same thing.
Leading up to the modern world, however, physical/exoteric alchemy has been set aside in favor of modern chemistry, and spiritual/esoteric alchemy as a purely non-physical pursuit of enlightenment has been heavily influenced by the writings of Carl Jung, who systematized alchemy as a metaphor for psychological development.
Today, Spiritual Alchemy can be further distinguished from Psychological Alchemy in that Spiritual Alchemy relies on spiritual or esoteric methodologies while Psychological Alchemy is the inheritor of Jung's systems.
The most important element of spiritual alchemy is always the alchemist. Each individual spiritual alchemist will eventually develop their own system, their own preference, and their own application for the work of personal transformation.
My system of spiritual alchemy is based on Aristotelian elemental theory (removed entirely from scientific understanding), and a system of 8 allegorical processes (based on a set of seven that have become relatively common for modern spiritual alchemists). I also use medieval and renaissance alchemical symbols as well as sigils of my own design as a way to express intention, initiate spiritual working, and establish spiritual boundaries between myself and the world around me.
My system requires an assumption of the presence of spiritual energy, spiritual entity, and and an assumption of the ability of the spirit to ineract with physical reality. My system also requires an assumption of spiritual energy as present within and intermingled with physical reality.
My system is not going to work for everyone. Some pieces of my system might work for some people. Others might use my system as an example of the kind of thing they might do and then establish their own personal practice which is completely different, founded on different elements, with or without the use of any kind of symbols.
Religions are organized groups, so your spiritual alchemy only counts as a religion if you belong to an organized group of spiritual alchemists who all share certain aspects of personal practice in common or share a common doctrine.
Generally speaking, spiritual alchemy is a type of spirituality, which is not organized. Spiritual alchemy can be an excellent complement to any religious path, as long as you choose to work with elements and systems that are appropriate for that path.
I personally see my spiritual alchemy as separate from my religious practice. My spiritual alchemy is how I interact with the world on a daily basis. My religious practice is how I interact with Divinity on a regular basis. Sometimes, they overlap or work together, but not always.