A Japanese grammar book will tell you that to make a 形容動詞(な adjective) into an adverb, you add に after it. For example:
However, recently, I’ve started to notice sentences where instead of に, で is used. For example:
This doesn’t make sense with me. It does not seem to be the で that marks “method” either. For me, it clearly should have been
Question: is the usage of で here grammatically incorrect? If not, then what’s the explanation of it(why not に, etc.) ?
Note: this question is SPECIFICALLY about the use of に and で after 形容動詞. Not just their general difference.