Māhiyyah (quiddity) concerns what a thing is, whereas external existence concerns its actually being present. Understanding the essence of a possible thing does not establish that it exists.
A created thing may be eternally known or within eternal power without being an eternally existent object. The phrase “bringing a nonexistent thing into existence” does not presuppose an already-existing physical object.
Power relates to the possible object, knowledge to what is known, and takwīn to the originated product. Each relation needs its own analysis; rules for one relation cannot automatically be transferred to another.