Weight Paint: you cannot select a bone if either Paint Mask or Vertex Selection is active.
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Since they look similar to vertex and face selection in good old Edit Mode, once one of them was active (not on purpose) I was not expecting that I can deactivate both at the same time, rather than always having one of them active.
Vertex Weights: this panel is only added to the vertex info (which looks the same otherwise) if you click on the vertex, not if you create a selection including only the vertex, e.g., by box-selecting over it.
(Concerns Blender Animation & Rigging course, Lecture Rigging & Weight Painting a Leg, from around time 6:16. I am using Blender 3.6.5 on Windows. )
