I think the GUI is only presenting what is contained inside the USD stage.
USD transforms (see the UsdGeomXformable class) can be 4x4 matrices or a number of individual transformation operations (scale, rotate, translate (SRT), orientation (quaternions)) and to make matters even more complicated, there can be an arbitrary long array of these individual transformation operations in a specific order which neither of these two GUI examples shows.
If you only wanted the SRT representation of the 4x4 transformation, it would be required to decompose that matrix into individual SRT operations which isn’t a bijective operation with Euler angles which seem to be used in that “Rotate” GUI line. That would need to be a quaternion orientation instead to make things more robust and that type using four floats is similarly unintuitive as the original 4x4 matrix.
Add animations in the mix and things get even more involved. This page describes some of the USD possibilities with transforms. Look for the xformOpOrder for example: https://openusd.org/release/tut_xforms.html
So to directly control the actual transformations contained inside the respective USD stage, there is either that matrix or the transform operations GUI.