" It's considered ungrammatical in formal English. What you've got in "not casual" is a rhetorical device called litotes, which is expressing an affirmative idea (here "formal") as its negation ("not casual"). You may use it and grammatically.
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Samir1Is "… but nonetheless not casual" a double-negative?No. You're thinking that 'none' in 'nonetheless' makes it the first negative and that 'not' (of course) is the second negative.