"I am not busy."
很 looks like a copula but I've asked around and it is not a copula but an adverb literally meaning "very" but usually without meaning when used in these kind of constructions.
Many languages don't use copulas with adjectives since their adjectives are more like verbs than the adjectives in European languages are. They are often called "stative verbs".
I also just learned in the comments of another question in this lesson that 很 is not used in questions or negative statements.
When you make an absolute negation in Chinese, it is not correct to talk about the magnitude, quantity, completion, etc. As I am not busy (at all), "busy" is inexistent and I cannot attach 很 and say 我很不忙 ↢wrong sentence
(The exceptions I can think of are some feelings and emotions. It is allowed to say 我很不开心/I am very unhappy, 我很不喜欢～/I don't like ~ very much.)
If I say 我不很忙，I am making a negation on "very", not busy. It means I am still busy, just not very busy.
I think in a thread another native user pointed out to you 很 does always mean "very". I agree with her.
I know a theory says it's a copula. I don't study linguistics, not even language academically. So I would hold back saying it's wrong. It didn't convince me anyway. If it is a copula, 2 questions need to be answered: (1) Why it disappears in so many sentence patterns? (2) Why it can always be replaced with a phrase of magnitude?
I am okay for courses to tell people to always insert a 很 - sometimes it is an inevitable evil to make things simpler for learning. However they should teach people it is a kind of mnemonics, not as a "rule", before they can explain things well.
There would be no literal translation you guys keep looking for. You always need to ensure the degree of magnitude is conceived explicitly or via the context for adjectives like this. So it depends on the circumstances in which you would say this sentence. Can you describe a scenario in details you would say it? Are you trying to highlight a comparison, or are you providing 2 parallel descriptions? Does that "you" know how tall that "I" is? And does that "you" know how tall he is himself?