Question about 種類

My textbook has the following sentence:

最近はおにぎりやスープなど、種類が増えています

So I know this means, "types of onigiri, soup, and other things are increasing", but I would have written it like:

最近はおにぎりやスープなどの種類が増えています or
最近はおにぎりやスープの種類が増えています (without the など)

I can't see the grammatical link between おにぎりやスープ and 種類. Does など serve this function? Hmm...

おにぎりやスープなど、種類が増えています
Types [of something] are increasing such as onigiri or soup.

おにぎりやスープなどの種類が増えています
Types of onigiri, soup, etc. are increasing.

おにぎりやスープの種類が増えています
Types of onigiri and soup are increasing.

I hope the above clarify the difference.

Got it! ありがとうございました！