Jade keeps talking about losing her powers, but even after the Green Sun's power is completely gone, she'll still be God Tier, won't she? She should still have a whole bunch of cool powers just like everyone else, even if she loses the First Guardian ones.

Yup! Her God Tier powers are intact. It may take her a while to figure out what exactly was Green Sun powered, and how to compensate for no longer having that boost, though.