Neither, both, Azathoth, Yog-Sothoth. Truly we don't know, because the story where the Supreme Archetype is mentioned is extremely vague and Lovecraft intentionally did that for most of his stories for readers to interpret on their own.
For starters, nothing is really happening in the mythos, as everything is a false illusion contorted by the archetypes
Time, the waves went on, is motionless, and without beginning or end. That it has motion, and is the cause of change, is an illusion. Indeed, it is itself really an illusion, for except to the narrow sight of beings in limited dimensions there are no such things as past, present, and future. Men think of time only because of what they call change, yet that too is illusion. All that was, and is, and is to be, exists simultaneously.
These revelations came with a godlike solemnity which left Carter unable to doubt. Even though they lay almost beyond his comprehension, he felt that they must be true in the light of that final cosmic reality which belies all local perspectives and narrow partial views; and he was familiar enough with profound speculations to be free from the bondage of local and partial conceptions. Had his whole quest not been based upon a faith in the unreality of the local and partial?
After an impressive pause the waves continued, saying that what the denizens of few-dimensioned zones call change is merely a function of their consciousness, which views the external world from various cosmic angles. As the shapes produced by the cutting of a cone seem to vary with the angles of cutting—being circle, ellipse, parabola, or hyperbola according to that angle, yet without any change in the cone itself—so do the local aspects of an unchanged and endless reality seem to change with the cosmic angle of regarding. To this variety of angles of consciousness the feeble beings of the inner worlds are slaves, since with rare exceptions they cannot learn to control them. Only a few students of forbidden things have gained inklings of this control, and have thereby conquered time and change. But the entities outside the Gates command all angles, and view the myriad parts of the cosmos in terms of fragmentary, change-involving perspective, or of the changeless totality beyond perspective, in accordance with their will.
Azathoth being played music by The Ultimate God's is an illusion, the being speaking to Randolph is an illusion, and change itself is an illusion, as everything is a fixed existence, because everything and anything inside the mythos is flattened into an indistinguishable everything that rids variability and differentially making everything identical
Paid attention to the conclusive summary sentence? We don't know if the Supreme Archetype itself, Yog, or some other character was actually present during what happened of the events of TTGOTSK. It's hinted at being Yog, but all its referred to is ENTITY but we don't know and we will never truly know, the scaling on the wiki is more of an educated guess if anything, Lovecraft never put a power system on his Yog or Azathoth so trying to scale one over the other is pretty meaningless.
