This is a good sensationalist title that could easily be changed to "Will using a VPN become illegal under the CFAA?" and like any such headlines, the answer is "no".
Just because one side is making an argument for that interpretation in a civil case means pretty much exactly nothing.
What's more, the Supreme Court in recent rulings has started to slap down overly broad interpretations of "hacking" under the CFAA. Notably, the court recently curtailed the definition of "unauthorized" use in van Buren [1], which to me was a welcome but somewhat unexpected ruling.
There's absolutely nothing to worry about here.
[1]: https://www.lawfareblog.com/supreme-court-reins-cfaa-van-bur...
EDIT: corrected van Buren characterization.