Is there any meaningful difference when という is added to わけ?
Neither of the lessons really mention it.
https://bunpro.jp/grammar_points/241 わけではない
https://bunpro.jp/grammar_points/537 というわけではない
From Wasabi’s article (https://www.wasabi-jpn.com/japanese-grammar/explanatory/) it just says that「という sometimes comes before わけではない”」. というわけだ is also a potential combination as well.