It has no negative or positive connotation, so you can consider it as neutral. It can of course be used in both a positive and negative manner but the connotation would be implied by the person using the word and the context. For example: 'He's such a bookworm, isn't it adorable.' (positive) 'He's such a bookworm, he needs to leave the house occasionally and play outside like a normal teenager.' (negative)

Since nobody's mentioned it, you should know that "bookworm" actually has a literal meaning. There are some insects and insect larva that can feed on the paste found in the bindings of books, even boring holes in them. I've never seen one of the ones that bores holes, but I have indeed had a little insect called a "silverfish" run out of a bookbinding.

It depends on the context and culture . Some people treat a bookworm as someone introvert and not outgoin and only reads books and boost his culture and education and don't have enough social skills. Other people treat a bookworm as someone who is cultured , clever , smart and will have a good future without judging the whole nature of his personality

It means that they are a person who LOVES to read books. Typically, if someone says you’re a bookworm, they are saying that they are able to appreciate your liking of books; it’s a good thing usually.

I see some people say in their profile. I guess they mean it as "curious about anything".