In ArcGIS Pro, attempts to change the positions of the 3D feature labels in a scene by modifying the offset values in the Label Class pane result in no change. This issue is represented in the image below. Although the label preview displays the new position when the values of Offset X, Offset Y and Offset Z are changed, the changes are not displayed in the scene. The label is not positioned correctly and the red arrow indicates where the new position of the label must be displayed.
This is expected behaviour in ArcGIS Pro. In the Label Class pane, most labelling options are disabled. For more information, refer to BUG - 000093727.
As a workaround, use the Shadow option to create a duplicate 3D feature label.
The image below shows the 3D feature label positioned correctly in the scene.
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