Rviz Interactive marker does not move towards y-axis

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when I manually try to move the robot with the interactive marker, the marker simply does not move towards y-axis.

The interactive marker, as used by the MoveIt RViz plugin, is a 6 DoF marker.

It's inherently impossible for a 5 DoF robot to reach all the poses a 6 DoF marker can assume.

That's the immediate cause of the behaviour you observe.

I thought the marker is not moving because I commanded the robot to move to an unreachable position,

Indeed.

But note: you're not commanding anything yet. The marker only alters the Goal State.

however since the Query panel succeeded to bring the robot to that position, I am clueless.

Using the <random valid> option from the dropdown instructs the MoveIt RViz plugin to chose a random joint space pose for the selected group.

As joint space poses will always be reachable -- no matter the nr of DoF -- this will work.

No IK is involved there, which would explain why you cannnot use the marker, but can set a random joint space pose successfully.