To what extend did Istari know Middle-earth?

[Galadriel55]

The Ainur know of the creation of the world. Gandalf was there when the world was shaped. So in his way, through the lens of his own part in the Song, he has knowledge of the true nature of the world and its creation.

The Valar, and the Maiar by proxy, do not have absolute knowledge of everything in Middle-earth, especially of events which occurred after the creation. For instance, they did not know about the awakening of Men. I suppose argument is to be made as to how much they knew and were subvertly involved in events of the Second and Third Ages, and whether or not Sauron's power did anything to counter that. But in either case Gandalf's knowledge is not going to be about what stone the Ring might have, but the underlying nature of the Ring and how it could affect people; the nature of Sauron and how he would think and act.