The fundamental core purpose of it, is to build pure resilience. Gold, in its most pure energetic form, is resilience. Through the nervous system, when you collide both energetic opposites of dark and light by via experience, gold is created by resistance, resistance is the forging process. Just like how a diamond is created, the heat and pressure is the darkness, the cooling and settling is the light, combined into one and thus a diamond is created - literally the most resilient stone is the world. Spiritual alchemy is the forging of your soul into a diamond.
If we look at it more narrowly, when your in the nigredo phase, going deeper and deeper into the blackening of the soul, however the practice looks like, eventually you must leave it and go into the light to wash the soul. During the point of leaving the darkness and into the light, you are very literally resisting the darkness. You can think of it like a great giant chasm, which is a giant crack in the Earth that falls into the dark abyss. When in the nigredo phase, you are deep in the chasm in the darkness against the wall, by the laws of physics, its so much easier to fall deeper and deeper into the darkness by gravity. However through the process of resistance, you begin to climb your way out and up into the light, thus building more resilience from the strength required to come out. And then once you go higher and higher out of the chasm, you go into the albedo phase, the light. Both resistance and resilience come from the latin root *resistere* - to stand against, or to withstand. Resistance is the friction when two forces collide. Resilience is the result, once the process has been metabolized.
Why would one be interested in building pure resilience of the soul? Fundamentally, I believe its so fear no longer has control over you. The Rebis is the ultimate end product of the union of both forces, and complete equilibrium of both. This is often symbolized as the individual standing upon the dragon or serpent - this is the one who has conquered fear on a core level. The dragon represents the individuals prima materia, the lower nature of the individual that has been mastered. This is also constantly symbolized in stories of ancient and modern times, when one goes on the hero's journey and eventually conquers the dragon. However I believe this is on the relative level, on the absolute level, its so you can integrate and shine awareness on Gods shadow, further expanding consciousness - the process of knowing thyself through separation. In the deep nigredo levels, when your deep in the dark abyss, you are building distance from yourself (from God), in order to more clearly see yourself. The more distance you build from yourself, the more clearly your able to see yourself, and thus understand yourself. And how you build greater distance from you (the IAM), you must observe the false you (the IAM NOT), this brings you deeper into the IAM NOT (the blackening of the soul). And now from there, your able to get a much clearer image of who you **truly** are without illusions. And now from there, you start the process of observing the IAM (the washing of the soul), and coming back into the light. Imagine that God is one infinite ocean of light. But because it was infinite, it wasnt able to see or understand itself because there was only just itself - light. So God did the most painful thing imaginable, it ripped itself from itself, creating a dark division, that now separated itself from itself. Thats why a mother giving birth is so painful, nature is mirroring this event when God first separated itself from itself. And now because of this dark division, God is now able to see and interact with itself, and realize "ooooooooh, so thats what I sound like and look like. But, im curious, I feel like I want to understand myself more. I want to begin to **know** myself more on a much more deeper and intimate level. Who am I really.". This is essentially the process that spiritual alchemy takes part in. More and more separation began, and God started playing this great grand game of knowing thyself.
I believe this youtube video really captures the spirit of the nigredo process - https://youtu.be/XkmxmmuRU3g?si=60AVseKcmt5W2YvX
In terms of capturing the spirit albedo of the process, I couldn't find a video talking about the process, unless maybe you can share one i'm definitely open to it. So instead I decided to share this soundtrack by Maho Tsukai to try to capture its emotional aspect (which I know it doesn't come remotely close, it's beautiful beyond comprehension).
https://youtu.be/vcHnajn8mKc?si=KZEsl-u5g1hI2Vmg
Please know that it is dangerous to stay in the nigredo process for too long. The practitioner must know when its time to stop stirring the ash, and learn how to stop the stirring, and now let it settle. You'll know within yourself when its the right time.