Getting index of item in items inside twig template
You can't, because the loop index is local. And you don't need a class with the index in the paragraph when you have it in the surrounding div for targeting it in CSS.

There is also a fundamental aspect with rendering referenced entities. They are cached and not necessarily rebuild when the order in the field changes. This is even more problematic for other entities than paragraphs, which can be used in more than one place in different orders.