Is the established perfection of Allah only that which is possible, and does this detract from Allah's greatness and divinity?

The questioner is correct in affirming the absolute perfection of Allah Almighty in all respects. We cannot conceive or grasp the details of this perfection, let alone encompass it with our knowledge.

That which is impossible is not a thing for power to relate to; rather, it is pure non-existence.

And Allah is Most Capable of all things. This thing inquired about is not a thing, for it is inherently impossible and unattainable. Power relates only to that which is possible, not to that which is necessary ( واجب ) or that which is impossible ( ممتنع ), because their existence or non-existence is necessitated by their very essence.

The fact that power does not relate to the impossible and unattainable does not contradict Allah's capability over all things, because the impossible and unattainable are not things in the first place.