As far as I understood the new package, in EU we will have to be charging different VATs depending on the destination country of the product. Am I correct? And will nopCommerce be able to support that from July 1st. 2021?
Sure. You already configure rates based on a destination.
Please see admin area > configuration > settings > tax settings > the "Tax based on" dropdownlist and the "VAT" block. And final rates can be configures in admin area > configuration > tax providers