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In the sidebar of Context view, do you see a "No Context" item? Stuff from the inbox should appear there.

The "Show in Context Mode" menu item does everything the "Context Mode" item does and a bit more. Specifically, if you have rows selected in Project mode, it attempts to keep those rows selected after the switch. When you're in Context mode, that menu item switches you back to Project mode.

(I mainly find that command useful when I want to select an action in Context mode, then flip back to Project mode and examine the project that action's from.)