I think you need to use depth=1 rather than depth=2.
You are specifying, via the child_of argument, that you want to display children of the current Page’s parent Page. That means that the first level of hierarchy is the current Page (and any of its siblings). The second level of hierarchy would be child pages of the current Page (and of any of the current Page’s siblings).
So, give depth=1 a try.
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