lord of the rings - How did Gandalf get his staff back after being captured by Saruman in Orthanc?

In the books, Gandalf has 2 staves.

The first one which he has all the way up to the encounter with the Balrog. This is broken at the Bridge of Khazad Dum when he breaks the bridge. That staff was presumably created in Valinor as part of his incarnation as a wizard.

The second one is created by Galadriel for him (along with his new white robes) after he returns from death and Gwaihir flies him to Lorien.

Staves are clearly very important receptacles/focuses of power. Saruman is significantly de-powered after Gandalf breaks his staff for example.

In the books, his staff wasn't taken from him. This may not have been in Saruman's power to do. When Gandalf later breaks Saruman's staff, it is clear it is not a trivial event to do it, but rather a ceremony or spell. Saruman can use the power of Orthanc to hold Gandalf, but not "defeat him" as such, unless he gets the One Ring.

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