When I choose a different object I don't see the associated nodes in the Shading tab change. I can see the Preview changes but not the nodes, notice the diffuse material is the same:
Q: What am I doing wrong here?
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You have pinned you node tree, that means that shader tree is always displayed for that editor regardless of 3D View selection.
Unpin it from the Shader Editor header by clicking the pin icon. This is useful when comparing materials, if two Node Editors are open, or to make sure you are editing a certain material regardless of selection, like say editing a particle material when the emitter is selected, or editing the material when an collection instance is selected.