Interesting. I don't have my copy of the letters at hand, so I can't quote directly, but I do know that Tolkien said that Gandalf's wanderings "out of thought and time" meant that he left the Circles of the World, and was sent back by "the Authority," aka Eru. Whether or not his journey from life and back included any time spent in Valinor, he does not say. But he was returned directly to the top of Zirak-zigil, literally naked, and was reclothed by Galadriel and the Elves of Lothlorien. One can presume that either Gandalf took Glamdring with him, or Gwaihir picked it up for him, but no mention of him having a staff with him is made. Therefore, it would appear to follow that the staff he had as Gandalf the White came from the Elves of Lothlorien. If it had any special "power," I would think it either came from Galadriel, or from Gandalf himself.
I have speculated in other writings that in the fashioning of these "signets of office," each of the wizards might have been required to place something of their own power into them, not to imbue them with mundane magical ability, but as a pledge to their position as Stewards. Others would not be able to use it to make magic, but it would give the wizards a taste of what they would be dealing with in the matter of the Rings, and perhaps make them more inclined to stick to their purpose, as the power would (by plan) be returned to them only when they returned to Valinor, and were able to resume their natural forms. This is wholly speculation, mind you; there's absolutely no proof to support it, except perhaps in Saruman's statement about Gandalf wanting the staffs of all the Five Wizards, which indicates some degree of more than symbolic importance to the items (this thought, of course, is contradicted by the puzzling fact that when Gandalf was a prisoner in Orthanc, Saruman let him keep his staff. We know this because he had it and used it, if I recall correctly, when Gwaihir plucked him off the top of the tower).
Ah, so much speculation, so little proof....
