Thanks for the extra information. If you are using the pivot tool you should not have to drag the gizmo it should automatically snap to the bounding box of the mesh. If there are instances of that static mesh then they will move based on the new pivot.
If you need to edit the pivot on multiple objects you could create a geometryScript, the current pivot tool will set the pivot to the center of the selected meshes not the individual center. Take a look at this video it might be closer to what you are looking for. UE5 Geometry Script - Y-to-Z-Up and Edit Pivot with an Asset Action - YouTube