Why Scharnhorst plans would not transform Japanese design

Would Scharnhorst-class plans have materially helped Japan design its capital ships?

No; Japan could already design more capable ships, even if Scharnhorst was among Germany's better large-warship efforts.

Japan did not need German help to design modern capital ships. Scharnhorst was one of Germany's stronger large-warship designs, but still inferior to what Japan could produce for its own requirements. Japanese designers already had the technical competence and strategic context to create more ambitious ships. Receiving the plans would therefore be an intelligence curiosity rather than a decisive transfer of naval architecture.