Newsguard seems to take a good approach. However, I also have the impression that Newsguard itself is not entirely open and transparent about what opinions and currents are represented there. The ratings sometimes seem a bit biased, while pages of dubious reputation sometimes come off surprisingly well.

No option to stop it's tab from opening automatically. (that I could find)

This widget requires massive amounts of work. Classifying news sources as "outright 100% true" and "outright 100% false" with their green/red mark label system is not the right way to do things.

They have very complete "Nutrition Labels" which allow for more complex ways to classify sites, so why don't they use them?

This can work but not for the time being. I highly discourage anyone from trying to get source guidance out of this widget in it's current state.

Based on the forementioned Nutrition Labels, they clearly have plenty of information on the sites they rate. All they have to do is use them more openly and make them simpler for a user to understand, instead of just putting them side to side and saying "This is great", "This is terrible".

This is an artifact of the current social mass hysteria against independent investigative reporting. Given the controversial reputation of the add-on no major surprises. Note there is no 'Yellow' tag, only Green or Red. The ratings are laughable. Many Green-rated sites were once-reputable but have abandoned journalistic standards such as: excessive reliance on anonymous sources, presenting opinion as fact, sourcing other media vs original sources, and failing to correct verifiable false statements.