The dock continues to work very well (so far!).
Unfortunately today the Surface lost touch with its pen again. After trying two restarts and opening various control panels related to the pen, I had to give up and use the “spare” tablet I had brought with me.
3 hours later, I woke the Surface up and it found its pen immediately.
Has anyone found a reliable way to help the Surface to find its pen again when it loses touch with it? (The pen battery level is fine.) On other tablets, when they lose touch with their pen, I have found that switching back and forth between laptop and tablet mode helps. Maybe what I should try with the Surface is attaching the keyboard and detaching it again!