This very short video shows the problem: https://photos.app.goo.gl/GzAnThMKZZ3Yp1x2A
The bit can not move completely due to interaction with the connector between the top and bottom mechanisms on the back.
Have I assembled something incorrectly, or is this a common problem? It is not a major issue, since all other places work, but since there is a puzzle with a bit in that position, I thought that it should work.