English |-n't| is also a negation that applies to what comes before. In fact I don't think you actually can put a verbal negation before the verb in English in ordinary/modern circumstances; only a few verbs can be directly negated, and if one of those isn't present, one is added (usually "do", this is called "do-support") ... and the negation goes after it.

"This is how you negate a verb" -> "This is not how you negate a verb" ('is' can be negated, the negation goes after)

"This confuses the duke" -> "This does not confuse the duke" ('confuses' wants do-support to negate it, and the negation goes after 'do'.)

You are right. However, I would argue that semantically the "do" is part of the negation.

Actually, you can do the same in German ("Ich tu nicht essen" -> "I do not eat"), but it's very colloquial and "forbidden" in writing. The proper form is "Ich esse nicht".