it soon becomes apparent that this would lead to chaos
I see nothing that could lead to chaos or disrupt user expectations. On the contrary, this is the most intuitive way to use it. When moving a node from one search node to another, only one thing should happen — the setting of parameters based on which the search was conducted. For the sake of security and stability, a restriction on dragging nodes with differing tags will suffice. In all other cases, the setting of properties described in the receiving search node is the expected behavior.
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I see nothing that could lead to chaos or disrupt user expectations. On the contrary, this is the most intuitive way to use it. When moving a node from one search node to another, only one thing should happen — the setting of parameters based on which the search was conducted. For the sake of security and stability, a restriction on dragging nodes with differing tags will suffice. In all other cases, the setting of properties described in the receiving search node is the expected behavior.