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At around 0:02 you can see them lower the stage onto the support truss that has been placed directly underneath it. (There's an earlier vertical shift, but it affected the entire view, like the camera was bumped/adjusted.) So at the start of the video the stage was being mostly supported by the crane.
Later in the day the stage was moved via crane to a separate "deservicing structure" where the stage can be semi-permanently affixed, fluids/gasses can be safely offloaded, etc.