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I mean, the nature of projects is that they consist of many actions, which may have different contexts.
Fixed it for you! Projects don't have contexts by default, but a default context can be assigned to the tasks assigned to a project. Bill pretty much describes the rationale for this feature in the last paragraph above.

Unchecking the 'Show Projects and Action Groups' in context mode in the Preferences>Data pane will hide them completely in context mode.