Like pretty much every moving part in this microscope, the XY specimen stage mechanism also suffered from dried/sticky grease, preventing the X axis from moving at all. As such like in the previous case, the only solution was to tear it down, clean it and apply new grease and oil.
The separation of the mechanism from the stage is simple: in the bottom of the geared side (where the knobs are) this forelock is moved as shown in the picture, and by moving the Y axis to the end of its travel range, the mechanism is removed: